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Stein fillings and SU(2) representations of the fundamental group

Banff International Research Station for Mathematical Innovation and Discovery

In recent work, Baldwin and I defined invariants of contact 3-manifolds with boundary in sutured instanton Floer homology. I will sketch the proof of a theorem about these invariants which is analogous to a result of Plamenevskaya in Heegaard Floer homology: if a 4-manifold admits several Stein structures with distinct Chern classes, then the invariants of the induced contact structures on its boundary are linearly independent. As a corollary, we conclude that if a homology sphere Y admits a Stein filling with nonzero first Chern class, then there is a nontrivial representation (\pi_1(Y) \to SU(2)\). This is joint work in progress with John Baldwin.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: Princeton University

2016-09-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59274

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/