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Stein fillings and SU(2) representations

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HTLW02 - 3-manifold workshop

Co-author: Steven Sivek (Imperial College)

I'll describe recent work with Sivek in which we prove that if a 3-manifold Y admits a Stein filling which is not a homology ball then its fundamental group admits a nontrivial SU(2) representation. Beyond establishing a new connection between contact geometry and the fundamental group, this result allows us to deduce the existence of nontrivial representations where previously existing methods do not appear to suffice. Our proof makes use of a fairly new invariant of contact 3-manifolds which Sivek and I defined in the context of instanton Floer homology.

This talk is part of the Isaac Newton Institute Seminar Series series.

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