Asian Journal of Mathematics

Volume 17 (2013)

Number 3

Floer homology for 2-torsion instanton invariants

Pages: 471 – 524

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n3.a5

Author

Hirofumi Sasahira (Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Japan)

Abstract

We construct a variant of Floer homology groups and prove a gluing formula for a variant of Donaldson invariants. As a corollary, the variant of Donaldson invariants is non-trivial for connected sums of 4-manifolds which satisfy a condition for Donaldson invariants. We also show a non-existence result of compact, spin 4-manifolds with boundary some homology 3-spheres and with certain intersection forms.

Keywords

instanton, Floer homology, torsion cohomology, dirac operator

2010 Mathematics Subject Classification

57R57, 57R58

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