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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
On representation varieties of $3$–manifold groups

Michael Kapovich and John J Millson

Geometry & Topology 21 (2017) 1931–1968
Abstract

We prove universality theorems (“Murphy’s laws”) for representation varieties of fundamental groups of closed 3–dimensional manifolds. We show that germs of  SL(2)–representation schemes of such groups are essentially the same as germs of schemes over of finite type.

Keywords
character varieties, $3$–manifold groups
Mathematical Subject Classification 2010
Primary: 14B12, 20F29, 57M05
References
Publication
Received: 13 September 2013
Revised: 31 May 2016
Accepted: 19 September 2016
Published: 19 May 2017
Proposed: Walter Neumann
Seconded: Ciprian Manolescu, Bruce Kleiner
Authors
Michael Kapovich
Department of Mathematics
University of California, Davis
1 Shields Ave
Davis, CA 95616
United States
Korea Institute for Advanced Study
207-43 Cheongnyangri-dong, Dongdaemun-gu, Seoul, South Korea
http://www.math.ucdavis.edu/~kapovich
John J Millson
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742
United States
http://www.math.umd.edu/~millson