Lagrangian correspondences and Donaldson’s TQFT construction of the Seiberg–Witten invariants of 3–manifolds

Nguyen, Timothy

doi:10.2140/agt.2014.14.863

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Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg–Witten invariants of $3$–manifolds

Timothy Nguyen

Algebraic & Geometric Topology 14 (2014) 863–923

DOI: 10.2140/agt.2014.14.863

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

Volume 14, issue 2 (2014)