Algebraic & Geometric Topology Volume 14, issue 2 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Bibliography

1	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
2	B Booß-Bavnbek, M Lesch, C Zhu, The Calderón projection: New definition and applications, J. Geom. Phys. 59 (2009) 784 MR2536846
3	S K Donaldson, Topological field theories and formulae of Casson and Meng–Taubes, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 87 MR1734402
4	S K Donaldson, Floer homology groups in Yang–Mills theory, Cambridge Tracts in Mathematics 147, Cambridge Univ. Press (2002) MR1883043
5	S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press (1990) MR1079726
6	O García-Prada, A direct existence proof for the vortex equations over a compact Riemann surface, Bull. London Math. Soc. 26 (1994) 88 MR1246476
7	M Hutchings, Y J Lee, Circle-valued Morse theory and Reidemeister torsion, Geom. Topol. 3 (1999) 369 MR1716272
8	P Kronheimer, T S Mrowka, Monopoles and three-manifolds, New Mathematical Monographs 10, Cambridge Univ. Press (2007) MR2388043
9	C Kutluhan, Y J Lee, C Taubes, $\mathit{HF}{=}\mathit{HM}$ I: Heegaard Floer homology and Seiberg–Witten Floer homology arXiv:1007.1979
10	M Lipyanskiy, A semi-infinite cycle construction of Floer homology, PhD thesis, MIT (2008)
11	R B Lockhart, R C McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985) 409 MR837256
12	T Mark, Torsion, TQFT, and Seiberg–Witten invariants of $3$–manifolds, Geom. Topol. 6 (2002) 27 MR1885588
13	G Meng, C H Taubes, Seiberg–Witten equations and the Milnor torsion, Math. Res. Lett. 3 (1996) 661 MR1418579
14	J W Morgan, T S Mrowka, D Ruberman, The $L^2$–moduli space and a vanishing theorem for Donaldson polynomial invariants, Monographs in Geometry and Topology, II, International Press (1994) MR1287851
15	J W Morgan, T S Mrowka, Z Szabó, Product formulas along $T^3$ for Seiberg–Witten invariants, Math. Res. Lett. 4 (1997) 915 MR1492130
16	J W Morgan, Z Szabó, C H Taubes, A product formula for the Seiberg–Witten invariants and the generalized Thom conjecture, J. Differential Geom. 44 (1996) 706 MR1438191
17	T S Mrowka, P Ozsváth, B Yu, Seiberg–Witten monopoles on Seifert fibered spaces, Comm. Anal. Geom. 5 (1997) 685 MR1611061
18	T Nguyen, The Seiberg–Witten equations on manifolds with boundary, PhD thesis, MIT (2011)
19	T Nguyen, The Seiberg–Witten equations on manifolds with boundary I: The space of monopoles and their boundary values, Comm. Anal. Geom. 20 (2012) 565 MR2974206
20	L I Nicolaescu, The Maslov index, the spectral flow, and decompositions of manifolds, Duke Math. J. 80 (1995) 485 MR1369400
21	L I Nicolaescu, Notes on Seiberg–Witten theory, Graduate Studies in Mathematics 28, Amer. Math. Soc. (2000) MR1787219
22	C H Taubes, Casson's invariant and gauge theory, J. Differential Geom. 31 (1990) 547 MR1037415
23	V Turaev, A combinatorial formulation for the Seiberg–Witten invariants of $3$–manifolds, Math. Res. Lett. 5 (1998) 583 MR1666856