Topology Seminar-On SU(2) representations of the fundamental groups of link complements
Thu, 20 March, 2025
4:45pm - 5:45pm
Time: Thursday March 20, 4:45-5:45pm
Place: Phillips Hall Room 414 A
Speaker: Boyu Zhang (UMD)
Title: On SU(2) representations of the fundamental groups of link complements
Abstract: Suppose L is a link in S^3. We show that the fundamental group of the complement of L admits an irreducible representation in SU(2)
that takes the meridians to traceless elements if and only if L is not the unknot, the Hopf link, or a connected sum of Hopf links.
As a corollary, the fundamental group admits an irreducible representation in SU(2) if and only if L is neither the unknot nor the Hopf link.
This result generalizes a theorem of Kronheimer and Mrowka to the case of links. The talk is based on joint work with Yi Xie.