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A menagerie of SU(2)-cyclic 3-manifolds

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Title: A menagerie of SU(2)-cyclic 3-manifolds
Authors: Sivek, S
Zentner, R
Item Type: Journal Article
Abstract: We classify SU(2)-cyclic and SU(2)-abelian 3-manifolds, for which every representation of the fundamental group into SU(2) has cyclic or abelian image, respectively, among geometric 3-manifolds that are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds that do not admit degree-1 maps to any Seifert Fibered manifold other than S3 or a lens space. We also produce infinitely many one-cusped hyperbolic manifolds with at least four SU(2)-cyclic Dehn fillings, one more than the number of cyclic fillings allowed by the cyclic surgery theorem.
Issue Date: 1-Jun-2022
Date of Acceptance: 28-Oct-2020
URI: http://hdl.handle.net/10044/1/87463
DOI: 10.1093/imrn/rnaa330
ISSN: 1073-7928
Publisher: Oxford University Press
Start Page: 8038
End Page: 8085
Journal / Book Title: International Mathematics Research Notices
Volume: 2022
Issue: 11
Copyright Statement: © The Author(s) 2021. Published by Oxford University Press. All rights reserved. This is a pre-copy-editing, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version is available online at: https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnaa330/6071861
Keywords: math.GT
math.GT
General Mathematics
0101 Pure Mathematics
Publication Status: Published
Online Publication Date: 2021-01-09
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics