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ISSN (electronic): 1464-8997
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Decision problems for $3$–manifolds and their fundamental groups

Matthias Aschenbrenner, Stefan Friedl and Henry Wilton

Geometry & Topology Monographs 19 (2015) 201–236

arXiv: 1405.6274

Abstract

We survey the status of some decision problems for 3–manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (word problem, conjugacy problem, isomorphism problem), and also the homeomorphism problem for 3–manifolds and the membership problem for 3–manifold groups.

Keywords
3-manifolds, fundamental groups, decision problems
Mathematical Subject Classification 2010
Primary: 57M05
References
Publication
Received: 16 February 2015
Accepted: 16 February 2015
Published: 29 December 2015
Authors
Matthias Aschenbrenner
University of California
Los Angeles, CA 90095
USA
Stefan Friedl
Fakultät für Mathematik
Universität Regensburg
D-93053 Regensburg
Germany
Henry Wilton
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
UK