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Published April 2002 | Version public
Journal Article Metadata-only

Seiberg–Witten and Casson–Walker Invariants for Rational Homology 3-Spheres

Creators

  • 1. ROR icon Max Planck Institute for Mathematics

Abstract

We consider a modified version of the Seiberg–Witten invariants for rational homology 3-spheres, obtained by adding to the original invariants a correction term which is a combination of η-invariants. We show that these modified invariants are topological invariants. We prove that an averaged version of these modified invariants equals the Casson–Walker invariant. In particular, this result proves an averaged version of a conjecture of Ozsváth and Szabó on the equivalence between their θ invariant and the Seiberg–Witten invariant of rational homology 3-spheres.

Additional Information

© 2002 Kluwer Academic Publishers. Received: 11 January 2001. Some of our arguments are inspired by the paper of Ozsváth and Szabó on the theta divisor and the Casson–Walker invariant. The first author is partially supported by the Humboldt Foundation (Sofja Kovalevskaya Award). The second author is supported by the Australian Research Council.

Additional details

Identifiers

Eprint ID
27446
DOI
10.1023/A:1016299716922
Resolver ID
CaltechAUTHORS:20111026-110403593

Funding

Humboldt Foundation Sofja Kovalevskaya Award
Australian Research Council

Dates

Created
2011-10-26
Created from EPrint's datestamp field
Updated
2021-11-09
Created from EPrint's last_modified field

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Mathematics Department