Seiberg-Witten theoretic invariants of lens spaces

1999/01/18 by Liviu I. Nicolaescu, Nicolaescu, Liviu I. · 2 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:11A99 #msc:53C20 #msc:53C25 #msc:57Q10 #msc:57R15 #msc:57R19 #msc:58D27 #msc:58G25 #msc:58G30

paper · pdf · doi:10.48550/arxiv.math/9901071

LaTex 2e with amssymb, 43 pages, 4 figures

arxiv created 1999/01/18 · arxiv updated 2009/11/30

Abstract

We describe an effective algorithm for computing Seiberg-Witen invariants of lens spaces. We apply it to two problems: (i) to compute the Froyshov invariants of a large family of lens spaces; (ii) to show that the knowledge of the Seiberg-Witten invariants of lens spaces is topologically equivalent to the knowledge of its Casson-Walker invariant and of its Milnor-Turaev torsion. We also use the results in problem (i) to derive several topological results concerning the negative definite manifolds bounding a given lens space.

Citations

• The Geometries of 3-Manifolds

Cited by

• Seiberg-Witten invariants of rational homology spheres
• Exact triangles in monopole homology and the Casson-Walker invariant

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