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Stein fillings and SU(2) representations

Presented by: 
John Baldwin Boston College, Boston College
Friday 3rd February 2017 - 14:00 to 15:00
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons