Stein fillings and SU(2) representations

Baldwin, John¹ ; Sivek, Steven²

¹ Department of Mathematics, Boston College, Chestnut Hill, MA, United States
² Department of Mathematics, Imperial College London, London, United Kingdom

Geometry & topology, Tome 22 (2018) no. 7, pp. 4307-4380.

Résumé

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 $SU\left(2\right)$. We give several new applications of these results, proving the existence of nontrivial and irreducible $SU\left(2\right)$ representations for a variety of $3$–manifold groups.

Détail

DOI : 10.2140/gt.2018.22.4307

Classification : 53D40, 53D10, 57R17, 57M27, 57R58
Keywords: contact structures, Stein fillings, instanton Floer homology

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