Geometry & Topology

On representation varieties of $3$–manifold groups

Michael Kapovich and John Millson

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

character varieties $3$–manifold groups


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.

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