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A lift of the Chern-Simons functional and its application to equivariant Floer homology

University of British Columbia

We investigate the gauge theory of 3- and 4- manifolds. A lift of the Chern-Simons functional for flat connections on a principal SU(2)-bundle over a homology 3-sphere Y is constructed, putting strong restrictions on the existence of low-dimensional instanton moduli spaces over the cylinder R x Y. The value of this lift is computed for the Brieskorn spheres Σ(p, q, pqk — 1), and there is found to be one and only one fiat con nection of Floer index 1 with positive Chern-Simons functional. This fact is applied to the computation of the equivariant Floer homology HFq,∗(Σ(2, 3, 6k — 1)) showing that there are connections of index 1 and 5 with non-trivial boundary in the equivariant Floer homology. Specializing to the case k = 2, we obtain vanishing ofHFg,₄∗₊₁(Σ(2,3, 11)).

Thesis/Dissertation

application/pdf

2009-04-15

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http://hdl.handle.net/2429/7136

Mathematics

University of British Columbia

UBCV

DSpace