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Speaker:
Hans Boden
Affiliation:
McMaster Univ./MPI
Date:
Mon, 18/06/2012 - 16:30 - 17:15
Location:
MPIM Lecture Hall
Parent event:
Geometric Topology Seminar In 1984, Casson constructed an invariant for homology 3-spheres by counting irreducible SU(2) representations, and he applied the invariant to the Hauptvermutung in dimension four. In 1992, X.-S. Lin defined a closely related invariant for knots by counting irreducible SU(2) representations of the knot group with meridional trace zero. Both invariants admit gauge theoretic interpretations leading to the refinements of Floer's instanton homology and to the knot Floer homology.
In this talk, I will give a brief survey of the invariants of Casson and Lin, and then discuss more recent work toward a Casson-Lin invariant of links, which was first defined for two component links using projective SU(2) representations by Harper and Saveliev, and then for links L with n ≥ 2 components using projective SU(N) representations in joint work with E. Harper. I will explain the compactness and irreducibility results needed to show the invariants are well-defined, and I will then outline computations of the invariants and a vanishing result for the invariants of split links.
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