Algebraic and Geometric Topology
Scope & Guideline
Connecting Algebraic Insights with Geometric Perspectives
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
Symmetry Integrability and Geometry-Methods and Applications
Advancing the Frontiers of Mathematical UnderstandingSymmetry Integrability and Geometry-Methods and Applications is a prominent open-access journal published by the NATIONAL ACADEMY OF SCIENCES OF UKRAINE, INSTITUTE OF MATHEMATICS, dedicated to advancing research in the fields of Analysis, Geometry and Topology, and Mathematical Physics. Since its inception in 2005, the journal has provided an esteemed platform for scholars from around the globe to share their innovative findings and methodologies, contributing to our understanding of complex mathematical concepts. With an impressive Q2 ranking in all three mathematical categories as per the 2023 Scopus rankings, the journal positions itself as a key resource for researchers seeking high-quality, peer-reviewed content. As a fully open-access publication, it ensures that research is readily available to a wide audience, fostering collaboration and knowledge exchange in the mathematical sciences.
Epijournal de Geometrie Algebrique
Bridging Theories and Applications in MathematicsEpijournal de Geometrie Algebrique is an esteemed open-access journal dedicated to advancing the fields of Algebra and Number Theory, as well as Geometry and Topology. Published by the CENTRE COMMUNICATION SCIENTIFIQUE DIRECTE-CCSD in France, this journal has gained recognition for its commitment to disseminating high-quality research since its inception in 2017. With an impressive positioning in the prestigious Q1 quartile for both categories as of 2023, it occupies a notable space in the academic landscape. The journal aims to provide a platform for scholars to share innovative findings and foster collaborations within the mathematical community. Researchers, professionals, and students will find valuable resources, insights, and a vibrant forum for discussion in this journal, which reflects the dynamic evolution of algebraic and geometric studies. Access to all articles is freely available, ensuring that knowledge is accessible to a broader audience, thus promoting ongoing discourse and discovery in these critical branches of mathematics.
Journal of the Institute of Mathematics of Jussieu
Advancing Mathematical Frontiers with Every PublicationJournal of the Institute of Mathematics of Jussieu, published by Cambridge University Press, is a leading academic journal that has established itself as a vital resource in the field of mathematics. With an impressive impact factor and a ranking in the top quartile (Q1) of miscellaneous mathematics, the journal serves as a platform for high-quality research from both established scholars and emerging researchers. Spanning from 2002 to 2024, the journal aims to foster collaboration and innovation in the mathematical community by publishing original research articles, reviews, and critical discussions on a wide range of mathematical topics. Although the journal does not offer open access, it remains widely accessible through various academic institutions and libraries, ensuring that critical advancements in mathematics are shared with a global audience. Located in the United Kingdom at the prestigious Cambridge campus, the journal reflects the rigorous standards of its publisher and the rich academic tradition of its home institution.
Journal of Homotopy and Related Structures
Pioneering Insights in Geometry and Number TheoryJournal 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.
Journal of Topology
Exploring the Dimensions of TopologyThe Journal of Topology, published by WILEY, is an esteemed peer-reviewed journal that has been at the forefront of the field since its inception in 2008. With an ISSN of 1753-8416 and an E-ISSN of 1753-8424, this journal is dedicated to the fundamental and applied aspects of topology, offering a platform for innovative research and critical findings in this vital area of mathematics. As a recognized leader in its category, the journal proudly holds a Q1 ranking in Geometry and Topology, reflecting its impact and contribution to the academic community, with a Scopus rank of #25 out of 106 in its field, placing it in the 76th percentile. Researchers and professionals can access high-quality articles that advance theoretical knowledge and practical applications, enhancing the mathematical literature and serving as a valuable resource for students and scholars alike. With ongoing publication until 2024, The Journal of Topology continues to shape the discourse in geometry and topology, making it an essential read for anyone involved in the field.
GEOMETRIAE DEDICATA
Exploring the Depths of Geometric ScienceGEOMETRIAE DEDICATA is a distinguished journal published by Springer, focusing on the intricate and dynamic field of geometry and topology. With an ISSN of 0046-5755 and an E-ISSN of 1572-9168, this journal has been a vital resource since its inception in 1972, continuing to provide insightful research up until 2024. Recognized for its scholarly contributions, it holds a Q3 category ranking in the field as of 2023, showcasing its commitment to advancing theoretical and applied geometrical investigations. Located in the Netherlands, specifically at VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, the journal offers its audience a platform to explore various aspects of geometry, encouraging interdisciplinary collaboration and knowledge dissemination. Although currently not an open-access journal, it is widely cited and respected in the academic community, making it an essential publication for researchers, students, and professionals devoted to expanding the boundaries of geometric science.
EXPOSITIONES MATHEMATICAE
Advancing Mathematical Frontiers with Rigorous ResearchEXPOSITIONES MATHEMATICAE, published by Elsevier GmbH, stands as a significant journal in the realm of mathematics, catering primarily to researchers, professionals, and students. With an ISSN of 0723-0869 and an E-ISSN of 1878-0792, this journal has made its mark in the academic community, boasting a Q2 classification in the miscellaneous mathematics category for 2023, illustrating its prominence within its field. The journal addresses a diverse scope of mathematical topics, encouraging the publication of original research and innovative theories while maintaining rigorous academic standards. As it converges from 2004 to 2024, EXPOSITIONES MATHEMATICAE continues to be an essential resource for advancing mathematical knowledge and fostering scholarly communication, despite being a non-open-access publication. Its location in Munich, Germany further anchors it within a rich intellectual tradition, providing accessibility for the mathematical community worldwide.
Homology Homotopy and Applications
Innovating the Future of Topological StudiesHomology Homotopy and Applications is a prestigious peer-reviewed journal published by INT PRESS BOSTON, INC, dedicated to advancing the field of mathematics, particularly within the realms of algebraic topology, homological algebra, and their applications. With an impressive Q1 classification in the mathematics category for the year 2023, this journal serves as a crucial platform for researchers, professionals, and students aiming to disseminate their findings in a rapidly evolving discipline. Although open access options are not currently available, the journal retains significant value with its rigorous selection process and high-impact studies. The journal invites submissions that explore theoretical developments as well as practical applications that bridge homology and homotopy theories, thus contributing to the broader scientific community from its base in the United States. With convergence covering years from 2001 to 2024, Homology Homotopy and Applications continues to be a vital resource for fresh insights and groundbreaking research in mathematical sciences.
QUARTERLY JOURNAL OF MATHEMATICS
Connecting Scholars through Rigorous ResearchQuarterly Journal of Mathematics, published by Oxford University Press, stands as a pivotal resource for the mathematical community, focusing on a broad spectrum of topics in the field of mathematics. With its esteemed history dating back to 1930, this journal continues to foster innovative research and discussions, providing a platform for scholars to share their findings and insights. Although the journal currently holds a Q3 classification in mathematics (miscellaneous) and is ranked #207 among general mathematics publications in the Scopus database, its commitment to quality and rigorous peer review ensures that it remains relevant and insightful. Researchers, professionals, and students alike will find the Quarterly Journal of Mathematics an invaluable tool for advancing knowledge and understanding in various mathematical disciplines, making it an essential addition to any academic library.
Pure and Applied Mathematics Quarterly
Advancing the Frontiers of Mathematical KnowledgePure and Applied Mathematics Quarterly is a prestigious journal published by INT PRESS BOSTON, INC, focusing on the diverse and evolving field of mathematics. Since its inception in 2007, this journal has grown significantly, currently holding a Q1 ranking in the Mathematics (Miscellaneous) category for 2023, positioning it among the leading publications in the discipline. With a commitment to publishing high-quality research, Pure and Applied Mathematics Quarterly fosters innovation and dialogue within the mathematical community by providing a platform for theoretical advancements and practical applications. The journal remains accessible to researchers and professionals through its ISSN 1558-8599 and E-ISSN 1558-8602, although it does not currently offer open access. As a vital resource for mathematicians, educators, and students, this journal endeavors to expand the frontiers of mathematical knowledge and contribute to the academic dialogue surrounding this fundamental science.