Algebraic and Geometric Topology
Scope & Guideline
Exploring the Boundaries of Algebra and Geometry
Introduction
Aims and Scopes
- Algebraic Topology:
Research often involves the study of topological invariants and their relationships to algebraic structures, such as homology and cohomology theories, spectral sequences, and operads. - Geometric Topology:
The journal features works that explore the properties and classifications of manifolds, knots, and links, including their geometric structures and embeddings. - Homotopy Theory:
A significant focus is placed on homotopy invariants, higher homotopy categories, and their applications to various mathematical fields including algebraic geometry and mathematical physics. - Representation Theory:
The interplay between topology and representation theory is a consistent theme, especially in understanding symmetries and actions on topological spaces. - Category Theory in Topology:
The journal often publishes papers that apply categorical frameworks to topology, enhancing the understanding of topological constructs via modern categorical methods. - Interdisciplinary Approaches:
Papers frequently intersect with other areas of mathematics, including algebra, combinatorics, and mathematical physics, demonstrating the broad impact of topological research.
Trending and Emerging
- Higher Homotopy Theory:
An increasing number of papers are exploring higher homotopy types and their implications, indicating a growing interest in understanding the nuanced structures that arise in higher dimensions. - Persistent Homology and Topological Data Analysis:
The application of topological methods to data analysis has gained momentum, with persistent homology becoming a popular tool for studying the shape of data and extracting meaningful features. - Equivariant Homotopy Theory:
Research focusing on equivariant aspects of topology, particularly in the context of group actions and symmetry, is emerging as a significant area of interest, reflecting its relevance in both algebraic and geometric contexts. - Categorical Approaches to Topology:
There is a marked increase in the use of category theory to frame topological questions, enhancing the understanding of relationships between different topological constructs and their algebraic counterparts. - Connections to Mathematical Physics:
An evident trend is the exploration of connections between topology and mathematical physics, particularly in areas like quantum topology and gauge theory, signaling a rich interplay between these fields.
Declining or Waning
- Classical Knot Theory:
There has been a noticeable reduction in publications solely focused on classical knot theory, as the field has evolved towards more complex interactions with other areas such as algebraic geometry and homotopy theory. - Elementary Topological Constructs:
Topics centered around basic constructions and introductory topology appear less frequently, possibly due to a shift towards more advanced and specialized areas of research. - Low-Dimensional Topology:
Research specifically targeting low-dimensional manifolds, such as 3-manifolds, has become less prominent, as researchers have begun exploring higher-dimensional analogs and more abstract topological concepts. - Traditional Cohomology Theories:
The focus on traditional cohomology theories has waned, with more emphasis now placed on derived and equivariant cohomology theories, reflecting a broader trend towards modern algebraic approaches.
Similar Journals
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
Exploring the Boundaries of Analysis and GeometryANNALS OF GLOBAL ANALYSIS AND GEOMETRY, published by Springer, stands as a prominent periodical in the fields of analysis and geometry, holding esteemed positions in the academic community with a consistent record since its inception in 1983. With an ISSN of 0232-704X and an E-ISSN of 1572-9060, this journal provides a platform for high-quality research articles that delve into the intricate relationships between geometric constructs and analytical methods. Despite the lack of open access, the journal's influence is noteworthy, evidenced by its 2023 category quartiles, achieving Q2 rankings in both Analysis and Geometry and Topology, and notable contributions to Political Science and International Relations as well. Its Scopus rankings further illustrate its impact, placing it at rank #60 in Geometry and Topology and #132 in Analysis within a competitive academic landscape. Researchers, professionals, and students alike will find ANNALS OF GLOBAL ANALYSIS AND GEOMETRY an invaluable resource for cutting-edge discoveries and scholarly discussions that push the boundaries of knowledge within these critical fields.
APPLIED CATEGORICAL STRUCTURES
Unveiling New Horizons in Algebra and Number TheoryApplied Categorical Structures is a prominent journal published by Springer, dedicated to the dissemination of high-quality research in the intersecting domains of algebra, number theory, and theoretical computer science. Since its inception in 1993, this journal has fostered academic discussion and innovation, contributing significantly to the advancement of categorical methodologies in these fields. With an impressive 2023 Q2 ranking in both Algebra and Number Theory, and Computer Science categories, it reflects a strong standing in the scientific community, positioning itself as a valuable resource for scholars. The absence of an Open Access model allows for a traditional subscription-based distribution, providing readers with curated, peer-reviewed articles that ensure academic integrity. Aspiring authors and researchers are encouraged to publish their work here, where their contributions will resonate across a vibrant network of professionals prioritizing cutting-edge development in categorical theory and its applications.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
Exploring the intricate ties of mathematics.JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, published by WORLD SCIENTIFIC PUBL CO PTE LTD, is a prominent academic journal dedicated to advancing the field of knot theory and its relationships with various mathematical disciplines. With its inception dating back to 1996, this journal serves as a vital platform for researchers, professionals, and students to share innovative findings and explore significant implications within the realms of Algebra and Number Theory. As of 2023, it is ranked in the third quartile (Q3) for its category, with Scopus ranking placing it at #89 out of 119 in Mathematics, demonstrating its role in shaping contemporary research perspectives. Located in Singapore, the journal is committed to fostering an environment where rigorous inquiry and collaboration can lead to meaningful advancements in mathematics. While it operates on a traditional access model, its comprehensive scope and esteemed reputation make it an essential resource for anyone seeking to deepen their understanding of knot theory and its ramifications.
SIAM Journal on Applied Algebra and Geometry
Exploring the Intersection of Algebra and GeometrySIAM Journal on Applied Algebra and Geometry, published by SIAM Publications, is a premier academic journal that occupies a vital space in the fields of Algebra, Geometry, and Applied Mathematics. With an impressive impact factor reflected in its Q1 category rankings in 2023 across key mathematical disciplines such as Algebra and Number Theory, as well as Geometry and Topology, this journal is positioned among the highest echelons of mathematical research. Since its inception in 2017, it has become a crucial source for advanced studies and applied techniques that harness algebraic and geometric methods, catering to both theoretical insights and practical applications. Researchers, professionals, and students alike benefit from its rigorous peer-reviewed articles that explore contemporary challenges and developments in mathematics. While Open Access options are currently not available, the journal remains dedicated to fostering innovation and knowledge dissemination within the scientific community, thus ensuring significant contributions to the advancement of the mathematical sciences.
Kodai Mathematical Journal
Nurturing Insights in Diverse Mathematical RealmsKodai Mathematical Journal is a distinguished publication dedicated to advancing the field of mathematics, particularly in miscellaneous areas. Established in 1949, this esteemed journal has been a reputable source for researchers and practitioners who seek to contribute to the rich landscape of mathematical knowledge. Published by KINOKUNIYA CO LTD, the journal is based in the academic environment of Tokyo Institute of Technology and serves a global audience with rigorous and insightful research articles. Despite its current Q3 quartile ranking in the Scopus Mathematics category, which reflects its niche but impactful contributions, the journal is poised for growth; the convergence of traditional and novel mathematical techniques promises to enhance its relevance further. Researchers, professionals, and students are encouraged to engage with the rich content of the journal, aimed at fostering collaboration and nurturing innovation in the mathematical community. While currently not available as Open Access, Kodai Mathematical Journal remains a critical resource for those passionate about mathematics and its applications.
Communications in Number Theory and Physics
Bridging the Gap Between Mathematics and PhysicsCommunications in Number Theory and Physics is a leading academic journal published by INT PRESS BOSTON, INC, dedicated to the exploration of the intersections between number theory and physics. Since its inception in 2007, the journal has established a reputation for excellence, evidenced by its 2023 rankings placing it in the Q2 category within the fields of Algebra and Number Theory, Mathematical Physics, and Physics and Astronomy (Miscellaneous). With an ISSN of 1931-4523 and an E-ISSN of 1931-4531, the journal facilitates valuable peer-reviewed research, making substantial contributions to both theoretical and applied aspects of its core disciplines. Recognized for its prominence within the academic community, it holds notable Scopus rankings, highlighting its influence and quality of published work. Communications in Number Theory and Physics serves as an essential platform for researchers, professionals, and students, fostering scholarly dialogue and advancing knowledge at the intersection of mathematics and physics.
JOURNAL OF GEOMETRIC ANALYSIS
Pioneering Innovative Approaches in Geometric AnalysisJOURNAL OF GEOMETRIC ANALYSIS, published by SPRINGER, stands as a premier platform for the dissemination of high-quality research in the field of geometric analysis. With its ISSN 1050-6926 and E-ISSN 1559-002X, this prestigious journal has maintained a robust academic reputation since its inception in 1991, boasting a convergence of ideas and research that will continue through 2024. It is categorized in the top quartile (Q1) of Geometry and Topology, highlighting its significance and influence in the mathematical community. Ranking 23rd out of 106 in its field, and placing in the 78th percentile according to Scopus metrics, this publication is essential for researchers, professionals, and students who seek to deepen their understanding of geometric structures and their applications. Though it operates under a subscription model rather than Open Access, the journal consistently aims to advance knowledge through rigorous peer-reviewed articles that explore the latest developments and methodologies in geometric analysis, making it a pivotal resource for anyone involved in mathematical research.
Quantum Topology
Unraveling the Mysteries of Geometry through a Quantum LensQuantum Topology is a leading journal in the interdisciplinary realms of geometry, topology, and mathematical physics, published by the European Mathematical Society. With an impressive H-Index that reflects its growing citation and recognition, this open-access journal has been committed to disseminating high-quality research since its inception in 2013, with full open access treatment commencing in 2021. Based in Germany, it serves as a platform for innovative studies that explore the intricate connections between quantum theory and topological structures. Achieving a notable Q1 category ranking in both Geometry and Topology and Mathematical Physics as indicated in the 2023 metrics, it ranks 31st out of 106 in the first category and 48th out of 85 in the latter, underscoring its importance in advancing scholarly dialogue in these fields. Researchers, professionals, and students alike are encouraged to contribute to and engage with the journal’s rich content, which not only includes original research articles but also review papers and significant theoretical advancements.
Journal of Homotopy and Related Structures
Exploring the Depths of Mathematical StructuresJournal of Homotopy and Related Structures is a distinguished academic journal published by Springer Heidelberg, specializing in the fields of algebra, number theory, geometry, and topology. With a focus on the intricate relationships and structures within these disciplines, the journal aims to facilitate the dissemination of original research and provide a platform for scholarly exchange among mathematicians. Since its inception in 2012, the journal has positioned itself in the Q2 category for both Algebra and Number Theory and Geometry and Topology in 2023, reflecting its growing influence and commitment to high-quality publications. Although it operates under a subscription model, the research published in this journal is highly cited, contributing to its notable rankings—#57 in Geometry and Topology and #65 in Algebra and Number Theory on the Scopus index. This journal is an essential resource for researchers, professionals, and students who wish to stay updated with the latest advancements and trends in homotopy theory and related mathematical structures.
TRANSFORMATION GROUPS
Illuminating the Path of Mathematical Discovery and InnovationTRANSFORMATION GROUPS, published by Springer Birkhäuser, is a leading academic journal specializing in the fields of algebra, geometry, and topology. With its ISSN 1083-4362 and E-ISSN 1531-586X, the journal has established itself as an essential resource for researchers and academicians, achieving a remarkable Impact Factor and ranking in prestigious categories: Q1 in Algebra and Number Theory and Q2 in Geometry and Topology as of 2023. Over its history from 1997 to 2024, TRANSFORMATION GROUPS has delivered cutting-edge research and innovative insights, currently holding Scopus rankings of #40/119 in Algebra and Number Theory and #38/106 in Geometry and Topology. This journal caters to those seeking to enhance their understanding of mathematical transformations and their applications, making it a vital platform for scholarly discourse within the mathematical community.