Geometry & Topology Volume 9, issue 4 (2005)

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Rohlin's invariant and gauge theory III. Homology 4–tori

Daniel Ruberman and Nikolai Saveliev

Geometry & Topology 9 (2005) 2079–2127

DOI: 10.2140/gt.2005.9.2079

Bibliography

1	P J Braam, S K Donaldson, Floer's work on instanton homology, knots and surgery, from: "The Floer memorial volume", Progr. Math. 133, Birkhäuser (1995) 195 MR1362829
2	K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1994) MR1324339
3	S E Cappell, R Lee, E Y Miller, Self-adjoint elliptic operators and manifold decompositions III: Determinant line bundles and Lagrangian intersection, Comm. Pure Appl. Math. 52 (1999) 543 MR1670052
4	S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
5	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
6	S K Donaldson, Floer homology groups in Yang–Mills theory, Cambridge Tracts in Mathematics 147, Cambridge University Press (2002) MR1883043
7	A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
8	M Furuta, Perturbation of moduli spaces of self-dual connections, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987) 275 MR914023
9	M Furuta, H Ohta, Differentiable structures on punctured 4–manifolds, Topology Appl. 51 (1993) 291 MR1237394
10	R E Gompf, T S Mrowka, Irreducible 4–manifolds need not be complex, Ann. of Math. $(2)$ 138 (1993) 61 MR1230927
11	C M Herald, Legendrian cobordism and Chern–Simons theory on 3–manifolds with boundary, Comm. Anal. Geom. 2 (1994) 337 MR1305710
12	J Milnor, D Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik und ihrer Grenzgebiete 73, Springer (1973) MR0506372
13	S J Kaplan, Constructing framed 4–manifolds with given almost framed boundaries, Trans. Amer. Math. Soc. 254 (1979) 237 MR539917
14	P B Kronheimer, Four-manifold invariants from higher-rank bundles, J. Differential Geom. 70 (2005) 59 MR2192061
15	P B Kronheimer, Instanton invariants and flat connections on the Kummer surface, Duke Math. J. 64 (1991) 229 MR1136374
16	E Laitinen, End homology and duality, Forum Math. 8 (1996) 121 MR1366538
17	C Lescop, Global surgery formula for the Casson–Walker invariant, Annals of Mathematics Studies 140, Princeton University Press (1996) MR1372947
18	K Masataka, Casson's knot invariant and gauge theory, Topology Appl. 112 (2001) 111 MR1823600
19	J W Milnor, Infinite cyclic coverings, from: "Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967)", Prindle, Weber & Schmidt, Boston (1968) 115 MR0242163
20	L Pontrjagin, Mappings of the three-dimensional sphere into an $n$–dimensional complex, C. R. $($Doklady$)$ Acad. Sci. URSS $($N. S.$)$ 34 (1942) 35 MR0008135
21	D Ruberman, Doubly slice knots and the Casson–Gordon invariants, Trans. Amer. Math. Soc. 279 (1983) 569 MR709569
22	D Ruberman, N Saveliev, Rohlin's invariant and gauge theory I: Homology 3–tori, Comment. Math. Helv. 79 (2004) 618 MR2081729
23	D Ruberman, N Saveliev, Rohlin's invariant and gauge theory II: Mapping tori, Geom. Topol. 8 (2004) 35 MR2033479
24	D Ruberman, N Saveliev, Casson-type invariants in dimension four, from: "Geometry and topology of manifolds", Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 281 MR2189939
25	D Ruberman, S Strle, Mod 2 Seiberg–Witten invariants of homology tori, Math. Res. Lett. 7 (2000) 789 MR1809302
26	C H Taubes, Gauge theory on asymptotically periodic 4–manifolds, J. Differential Geom. 25 (1987) 363 MR882829
27	C H Taubes, Casson's invariant and gauge theory, J. Differential Geom. 31 (1990) 547 MR1037415
28	V G Turaev, Cohomology rings, linking coefficient forms and invariants of spin structures in three-dimensional manifolds, Mat. Sb. $($N.S.$)$ 120(162) (1983) 68, 143 MR687337
29	K K Uhlenbeck, Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982) 31 MR648356
30	E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021