Seminar on Seiberg-Witten invariants and stable homotopy theory

Wintersemester 2002/03

M. Furuta and D. Kotschick

• Time and place: Tuesdays, 11 AM - 1 PM, room 251
• First meeting: 29 October 2002
• Contents: We shall discuss the stable homotopy version of Seiberg-Witten theory, for both 3- and 4-dimensional manifolds. After an introduction to Seiberg-Witten theory and the technique of finite-dimensional approximation, our main aim will be to understand Manolescu's construction of the Seiberg-Witten-Floer homotopy type of a rational homology 3-sphere.
• References:

  [F]	M. Furuta: Monopole equation and the 11/8-conjecture. Math. Res. Lett. 8 (2001), no. 3, 279--291.
  [BF]	S. Bauer and M. Furuta: A stable cohomotopy refinement of Seiberg-Witten invariants: I, Preprint math.DG/0204340.
  [M]	C. Manolescu: Seiberg-Witten-Floer stable homotopy type of three-manifolds with b1=0, Preprint math.DG/0104024.
  [KM]	P. B. Kronheimer and C. Manolescu: Periodic Floer pro-spectra from the Seiberg-Witten equations, Preprint math.DG/0203243.

• Intended audience: Diplom-, Master and doctoral students with an interest and some background in topology and geometry.
• Prerequisites: Some knowledge of differential geometry and geometric analysis, and of algebraic topology.
• Seminar plan
• Lecture notes (can only be accessed from within the department)