The 10/8ths Theorem
Seiberg-Witten theory and equivariant K-theory
Learning seminar, Spring 2019
The details: this is the webpage for a learning seminar on Furuta's paper [Fur01],
which uses Seiberg-Witten theory and equivariant K-theory to prove the 10/8ths theorem on the
intersection forms of spin 4-manifolds.
This seminar is organized by Arun Debray and Riccardo Pedrotti.
- Where and when: Mondays 10AM in PMA 9.166.
- Lecture notes can be found here.
- Planning meeting and overview
- Arun and Riccardo, January 23
- Compactness of the Seiberg-Witten moduli space
- Kai and Riccardo, January 28 and February 4
- The Pin2–-symmetry of the Seiberg-Witten equations
- Arun, February 11
- Finite-dimensional approximation
- Cameron and Leon, February 18 and 25
- Equivariant K-theory
- Richard, March 4
- Proof of the 10/8ths theorem
- Arun, March 11
- Z/2p-actions on spin 4-manifolds
- Arun and Jeffrey, March 25 and April 1
- Bauer-Furuta invariants
- Jeffrey, Leon, and Riccardo, April 15, April 22, April 29
- Families Seiberg-Witten invariants
- Arun, May 6
- S. Bauer and M. Furuta. A stable cohomotopy refinement of
Seiberg-Witten invariants: I. Invent. math. (2004) 155: 1.
- S. Bauer. A stable cohomotopy refinement of Seiberg-Witten
invariants: II. Invent. math. (2004) 155: 21.
- Jim Bryan, Seiberg-Witten theory and
Z/2p actions on spin 4-manifolds. Math. Res. Lett., 5(2):165–183, 1998.
- M. Furuta. Monopole equation and the 11/8-conjecture. Math. Res. Lett., 8(3):279–291, 2001.
- David Baraglia and Hokuto Konno. On the Bauer-Furuta and
Seiberg-Witten invariants of families of 4-manifolds.
- Michael J. Hopkins, Jianfeng Lin, XiaoLin Danny Shi, and Zhouli Xu. Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant
- Tian-Jun Li and Ai-Ko Liu. Family Seiberg–Witten invariants
and wall crossing formulas. Comm. Analysis and Geometry, Volum 9, Number 4, 777-823, 2001.
- Nobuhiko Nakamura, The Seiberg-Witten equations for families and diffeomorphisms
of 4-manifolds. Asian J. Math. 7 (2003) 133-138, Correction: Asian J. Math. 9 (2005) 185-186.
Markus Szymik. Characteristic cohomotopy
classes for families of 4-manifolds. Forum Mathematicum, 22.3 (2010): 509-523.
- Markus Szymik, The stable homotopy theory of vortices on Riemann