Volume 14, issue 2 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg–Witten invariants of $3$–manifolds

Timothy Nguyen

Algebraic & Geometric Topology 14 (2014) 863–923
Abstract

Using Morse–Bott techniques adapted to the gauge-theoretic setting, we show that the limiting boundary values of the space of finite energy monopoles on a connected 3–manifold with at least two cylindrical ends provides an immersed Lagrangian submanifold of the vortex moduli space at infinity. By studying the signed intersections of such Lagrangians, we supply the analytic details of Donaldson’s TQFT construction of the Seiberg–Witten invariants of a closed 3–manifold.

Keywords
Seiberg–Witten invariants, Lagrangian correspondences
Mathematical Subject Classification 2010
Primary: 53C05
Secondary: 53D12
References
Publication
Received: 27 July 2012
Revised: 3 July 2013
Accepted: 2 September 2013
Published: 31 January 2014
Authors
Timothy Nguyen
Simons Center for Geometry and Physics
State University of New York
Stony Brook, NY 11794-3636
USA