Jae Choon Cha is a Professor of Mathematics and Director of Center for Research in Topology at POSTECH. Also, he is an Affiliate Professor at KIAS and the Editor-in-Chief of the Bulletin of the Korean Mathematical Society.
- MATH 624 Algebraic Topology II
Note: for the first two weeks or longer, the course will be on-line based, by the decision of the university concerning COVID-19. See the course homepage for related information and materials for MATH 624.
- Lecture Notes: Introduction to Geometric Topology
2018 Spring at POSTECH
KnotInfo: a table of invariants of classical knots, maintained by Charles Livingston and me.
- Primary decomposition for topologically slice knots, The 15th East Asian Conference on Geometric Topology, February 12, 2020, RIMS, Kyoto, Japan.
- 공간의 현대적 수학 (Modern mathematics of spaces), 대한수학회 수학콘서트 (Mathematical Concert of the Korean Mathematical Society), October 25, 2019, Hongik University, Seoul, Korea.
- 공간의 수학 (Mathematics of spaces), IBS-CGP 수학 문화 강연 (IBS-CGP Mathematical Cultural Lecture), October 19, 2019, Pohang City Hall, Pohang, Korea.
- Primary decomposition for topologically slice knots, Four Manifolds: Confluence of High and Low Dimensions, July 11, 2019, Fields Institute, Toronto, Ontario, Canada.
- Filtering and decomposing the smooth concordance group of topologically slice knots, AIM workshop: smooth concordance classes of topologically slice knots, June 3, 2019, American Institute of Mathematics, San Jose, California, USA.
- Transfinite lower central series and Milnor invariants of 3-manifolds, Johnson homomorphisms and related topics 2019, May 14, 2019, University of Tokyo, Tokyo, Japan.
- 공간의 현대적 수학 (Modern mathematics of spaces), 무은재기념강연 (Mueunjae Memorial Lecture), April 25, 2019, POSTECH, Pohang, Korea.
- Homotopical properties and freely slicing good boundary links, Low dimensional topology and number theory XI, March 13, 2019, Osaka University, Osaka, Japan.
- Freely slicing good boundary links with a homotopy trivial plus property, Topology of Manifolds: Interactions between high and low dimensional topology, January 18, 2019, MATRIX Research Institute, Creswick, Victoria, Australia.
- Localization of groups and Milnor invariants of 3-manifolds, Workshop ⌈New Development of low-dimensional topology⌋, December 8, 2018, Hakone, Japan.
- 4-dimensional $L^2$-acyclic bordism, Seoul-Tokyo conference, December 1, 2018, KIAS, Seoul, Korea.
- Hirzebruch-type $L^2$-signature defects and topology of dimension 3 and 4, 2018 Joint Meeting of Korean Mathematical Society and German Mathematical Society, October 4, 2018, Seoul, Korea.
- Program Committee, The 15th East Asian Conference on Geometric Topology, February 10-13, 2020, RIMS, Kyoto University, Japan.
- Program Committee, The 14th East Asian Conference on Geometric Topology, January 21-24, 2019, Peking University, Beijing, China.
- Co-organizer, 2018 Mini-workshop on Low Dimensional Topology, September 14-15, 2018, POSTECH, Pohang, Korea.
- Co-organizer, Hyperbolic 3-manifolds and Related Topics, June 18-22, 2018, POSTECH, Pohang, Korea.
- A topological approach to Cheeger-Gromov universal bounds for von Neumann ρ-invariants
Communications on Pure and Applied Mathematics 69 (2016), no. 6, 1154–1209.
• Published • Preprint arXiv:1405.1805
- Casson towers and slice links (with Mark Powell)
Inventiones Mathematicae 205 (2016), no.2, 413–457.
• Published • Preprint arXiv:1411.1621
- Covering link calculus and the bipolar filtration of topologically slice links (with Mark Powell)
Geometry and Topology 18 (2014), no. 3, 1539–1579.
• Published • Preprint arXiv:1212.5011
- $L^2$-signatures, homology localization, and amenable groups (with Kent E. Orr)
Communications on Pure and Applied Mathematics 65 (2012), no. 6, 790–832.
• Published • Preprint arXiv:0910.3700
- Link concordance, homology cobordism, and Hirzebruch-type defects from iterated $p$-covers
Journal of the European Mathematical Society (JEMS) 12 (2010), no. 3, 555–610.
• Published • Preprint arXiv:0705.0088
- Injectivity theorems and algebraic closures with coefficients
Proceedings of the London Mathematical Society 96 (2008), no. 1, 227–250.
• Published • Preprint arXiv:math/0609409
- The structure of the rational concordance group of knots
Memoirs of the American Mathematical Society 189 (2007), no. 885, x+95pp.
• Published • Google Books • Preprint arXiv:math/0609408
List of all papers
- Transfinite Milnor invariants for 3-manifolds (with Kent E. Orr)
• Preprint arxiv:2002.03208 (54 pages)
- Primary decomposition in the smooth concordance group of topologically slice knots
• Preprint arxiv:1910.14629 (35 pages)
- Two-solvable and two-bipolar knots with large four-genera (with Allison N. Miller and Mark Powell)
Mathematical Research Letters, to appear
• Preprint arxiv:1901.02060 (31 pages)
- A family of freely slice good boundary links (with Min Hoon Kim and Mark Powell)
Mathematische Annalen 376 (2020), 1009–1030.
• Published • Preprint arxiv:1807.05474
- The bipolar filtration of topologically slice knots (with Min Hoon Kim)
• Preprint arxiv:1710.07803 (23 pages)
- Unknotted gropes, Whitney towers, and doubly slicing knots (with Taehee Kim)
Transactions of the American Mathematical Society 371 (2019), 2383–2429.
• Published • Preprint arXiv:1612.02226