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KNOTS in WASHINGTON 10 Japan-USA; workshop in Knot Theory
January 23-30, 2000
George Washington University
Washington, DC, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

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Link invariant from representation variety
by
Weiping Li
Oklahoma State University

In this talk, we show that the representation varieties of \pi1(S2 \(S2 \cap L)) (a link L in S3) with different conjugacy classes in SU(2) along meridians are symplectic stratified varieties from the group cohomology point of view. The variety can be identified with the moduli space of s-equivalence classes of stable parabolic bundles over S2 \(S2 \cap L) with corresponding weights along punctures, and also can be identified with the moduli space of gauge equivalence classes of SU(2)-flat connections with prescribed holonomies along punctures. We obtain an invariant of links (knots) from intersection theory on such a moduli space (a generalization of the signature of the link).

http://www.math.okstate.edu/~wli/

Date received: January 24, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caea-19.