Stein fillings and SU(2) representations
arXiv:1611.05629 · doi:10.2140/gt.2018.22.4307
Abstract
We recently defined invariants of contact 3-manifolds using a version of instanton Floer homology for sutured manifolds. In this paper, we prove that if several contact structures on a 3-manifold are induced by Stein structures on a single 4-manifold with distinct Chern classes modulo torsion then their contact invariants in sutured instanton homology are linearly independent. As a corollary, we show that if a 3-manifold bounds a Stein domain that is not an integer homology ball then its fundamental group admits a nontrivial homomorphism to SU(2). We give several new applications of these results, proving the existence of nontrivial and irreducible SU(2) representations for a variety of 3-manifold groups.
53 pages, 8 figures
References in corpus (1)
Cited by in corpus (9)
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- Instanton Floer homology of almost-rational plumbings
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- L-space knots are fibered and strongly quasipositive
- 2-torsion in instanton Floer homology
- Torus knots, the A-polynomial, and SL(2,C)
- Small Heegaard genus and SU(2)