Algebraic & Geometric Topology

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

Timothy Nguyen

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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.

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 2 (2014), 863-923.

Dates
Received: 27 July 2012
Revised: 3 July 2013
Accepted: 2 September 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715852

Digital Object Identifier
doi:10.2140/agt.2014.14.863

Mathematical Reviews number (MathSciNet)
MR3160606

Zentralblatt MATH identifier
1286.53031

Subjects
Primary: 53C05: Connections, general theory
Secondary: 53D12: Lagrangian submanifolds; Maslov index

Keywords
Seiberg–Witten invariants Lagrangian correspondences

Citation

Nguyen, Timothy. Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg–Witten invariants of $3$–manifolds. Algebr. Geom. Topol. 14 (2014), no. 2, 863--923. doi:10.2140/agt.2014.14.863. https://projecteuclid.org/euclid.agt/1513715852


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