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Stein fillings and SU(2) representations

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Title: Stein fillings and SU(2) representations
Authors: Baldwin, JA
Sivek, S
Item Type: Journal Article
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.
Issue Date: 6-Dec-2018
Date of Acceptance: 8-Apr-2018
URI: http://hdl.handle.net/10044/1/58969
DOI: https://doi.org/10.2140/gt.2018.22.4307
ISSN: 1364-0380
Publisher: Mathematical Sciences Publishers
Start Page: 4307
End Page: 4380
Journal / Book Title: Geometry and Topology
Volume: 22
Issue: 7
Copyright Statement: © Copyright 2018 Mathematical Sciences Publishers. All rights reserved.
Keywords: math.SG
math.GT
math.SG
math.SG
math.GT
Geological & Geomatics Engineering
0101 Pure Mathematics
Notes: 53 pages, 8 figures
Publication Status: Published
Online Publication Date: 2018-12-06
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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