Gauge Theory and Topology: The existence of irreducible SU(2) representations of link groups

Gauge Theory and Topology Seminar, SEMINARS

Speaker:

Boyu Zhang - University of Maryland

Representations of 3-manifold groups into groups such as SU(2) and SL(2,C) have been actively studied for decades.  Many topological invariants are defined by considering these representations, such as the Casson invariant, the Casson-Lin invariant, and the A polynomial.  In 2010, Kronheimer-Mrowka showed that the fundamental group of every non-trivial knot in S^3 admits an irreducible representation in SU(2) such that the image of the meridian is traceless, which answered a conjecture of Cooper.  In this talk, I will present a result that generalizes Kronheimer-Mrowka’s theorem to the case of links.  We show that for every link L that is not the unknot, the Hopf link, or a connected sum of Hops links, its fundamental group admits an irreducible SU(2) representation such that the image of every meridian is traceless.  The proof is based on an excision formula of singular instanton Floer homology.  This is joint work with Yi Xie.