Representations to finite groups and characteristic varieties

Daniel Matei

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

Conference Homepage

Representations to finite groups and characteristic varieties
by
Daniel Matei
University of Rochester
Coauthors: Alex Suciu (Northeastern University)

In a paper from 1935, Philip Hall introduced an invariant of finitely presented groups that counts representations onto finite groups. Let G be a finitely presented group with torsion-free abelianization (for example a link group). Following an idea of Fox, we compute Hall's invariant for certain metabelian representations in terms of the characteristic varieties of the group G. These varieties are defined by the Alexander ideals of G. As an application, we count the number of low-index subgroups of G. We also interpret the distribution of the prime-index normal subgroups of G, according to their abelianization, in terms of the characteristic varieties of G.

Date received: January 13, 2000