Geometry & Topology

On representation varieties of $3$–manifold groups

Michael Kapovich and John Millson

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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.

Article information

Source
Geom. Topol., Volume 21, Number 4 (2017), 1931-1968.

Dates
Received: 13 September 2013
Revised: 31 May 2016
Accepted: 19 September 2016
First available in Project Euclid: 19 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1508437634

Digital Object Identifier
doi:10.2140/gt.2017.21.1931

Mathematical Reviews number (MathSciNet)
MR3654101

Zentralblatt MATH identifier
1379.57003

Subjects
Primary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 20F29: Representations of groups as automorphism groups of algebraic systems 57M05: Fundamental group, presentations, free differential calculus

Keywords
character varieties $3$–manifold groups

Citation

Kapovich, Michael; Millson, John. On representation varieties of $3$–manifold groups. Geom. Topol. 21 (2017), no. 4, 1931--1968. doi:10.2140/gt.2017.21.1931. https://projecteuclid.org/euclid.gt/1508437634


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