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Rohlin's invariant and
gauge theory III. Homology 4–tori
Daniel Ruberman and Nikolai Saveliev |
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Geometry & Topology 9 (2005) 2079–2127
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arXiv: math.GT/0404162 |
Abstract |
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This is the third in our series of papers relating gauge theoretic invariants of certain –manifolds with invariants of –manifolds derived from Rohlin’s theorem. Such relations are well-known in dimension three, starting with Casson’s integral lift of the Rohlin invariant of a homology sphere. We consider two invariants of a spin –manifold that has the integral homology of a –torus. The first is a degree zero Donaldson invariant, counting flat connections on a certain –bundle. The second, which depends on the choice of a 1–dimensional cohomology class, is a combination of Rohlin invariants of a –manifold carrying the dual homology class. We prove that these invariants, suitably normalized, agree modulo 2, by showing that they coincide with the quadruple cup product of 1–dimensional cohomology classes. |
Keywords
Rohlin invariant, Donaldson invariant, equivariant
perturbation, homology torus
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Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57R58
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References |
Forward citations |
Publication
Received: 2 August 2005
Accepted: 25 October 2005
Published: 27 October 2005
Proposed: Ronald Stern
Seconded: Ronald Fintushel, Simon Donaldson
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Authors |
| Daniel Ruberman | |
| Department of Mathematics MS 050 Brandeis University Waltham MA 02454 USA |
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| Nikolai Saveliev | |
| Department of Mathematics University of Miami PO Box 249085 Coral Gables Florida 33124 USA |
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