Topology
Topology studies properties of spaces that are preserved under continuous deformations, and is one of the core foundational fields of modern mathematics. Major branches include point-set topology, algebraic topology, differential topology, and geometric topology. Algebraic topology uses algebraic tools such as groups and homology to characterize the shape of spaces, differential topology studies the structure of differentiable manifolds, and geometric topology focuses on the classification and properties of low-dimensional manifolds. Topology deeply intersects with algebraic geometry, differential geometry, and mathematical physics, and has broad applications in data science, robotics, and machine learning.
Research Progress
Mark your research stage in this field. Just a rough outline.
领域资源
Recent Publications
Source:: arXivAuthor A, Author B · 2026-08-15
This paper presents recent developments and open problems in the field, with new results on key conjectures.
Researcher C, Researcher D · 2026-07-22
We introduce a novel approach that unifies several classical results, providing new insights into long-standing questions.
Papers fetched from arXiv API automatically, for reference only. Updated periodically.
全球最好的大学项目
University of California, Berkeley
Department of Mathematics — Topology
United States · PhD
University of California, Berkeley maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Ian Agol, Peter Teichner contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
University of Cambridge
纯粹数学与数理统计系 — Topology
United Kingdom · PhD
University of Cambridge maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Oscar Randal-Williams, Henry Wilton contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
University of Chicago
Department of Mathematics — Topology
United States · PhD
University of Chicago maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including J. Peter May, Benson Farb contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
ETH Zurich
Department of Mathematics — Topology
Switzerland · PhD
ETH Zurich maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Thomas Willwacher, Ana Cannas da Silva contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
Harvard University
Department of Mathematics — Topology
United States · PhD
Harvard University maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Michael Hopkins, Peter Kronheimer contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
Massachusetts Institute of Technology
Department of Mathematics — Topology
United States · PhD
Massachusetts Institute of Technology maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Paul Seidel, Jeremy Hahn contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
University of Oxford
数学研究所 — Topology
United Kingdom · PhD
University of Oxford maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Martin Bridson, Marc Lackenby contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
Princeton University
Department of Mathematics — Topology
United States · PhD
Princeton University maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including David Gabai, Peter Ozsváth contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
Stanford University
Department of Mathematics — Topology
United States · PhD
Stanford University maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Ciprian Manolescu, Gunnar Carlsson contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
University of California, Los Angeles
Department of Mathematics — Topology
United States · PhD
University of California, Los Angeles maintains an active research program in Topology, with strengths spanning the core areas of the field. Faculty including Michael Hill, Sucharit Sarkar contribute to前沿 research at the intersection of theory and applications. The program offers doctoral training with access to specialized seminars and research groups.
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