Triangle Topology Seminar
Tuesday, November 13, 2018, 3:30pm, SAS 2102 (NCSU)
John Baldwin (Boston College, Mathematics)
Contact structures, instantons, and SU(2) representations

Abstract:

A strengthening of the Poincare Conjecture asks whether the fundamental group of every closed 3-manifold which is not the 3-sphere admits a nontrivial homomorphism to SU(2). With that as motivation, I'll describe a connection between Stein fillings of a 3-manifold and SU(2) representations of its fundamental group, coming from instanton Floer homology. This connection can be used to prove the existence of nontrivial SU(2) representations for all Seifert fibered spaces (reproducing a result of Fintushel and Stern) and much more! I'll end with a discussion of how these techniques may also be useful in computing instanton Floer homology (and in proving that it agrees with other Floer homology theories in some cases). This work is joint with Steven Sivek.

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