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.


Lecture schedule:

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.

Related links:

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 Mahowald Invariant.
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 surfaces.