Essential surfaces in highly twisted link complements

Ryan Blair; David Futer; Maggy Tomova

doi:10.2140/agt.2015.15.1501

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Essential surfaces in highly twisted link complements

Journal article

Open access

Peer reviewed

Essential surfaces in highly twisted link complements

Ryan Blair, David Futer and Maggy Tomova

Algebraic & geometric topology, Vol.15(3), pp.1501-1523

01/01/2015

DOI: 10.2140/agt.2015.15.1501

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Abstract

We prove that in the complement of a highly twisted link, all closed, essential, meridionally incompressible surfaces must have high genus. The genus bound is proportional to the number of crossings per twist region. A similar result holds for surfaces with meridional boundary: such a surface either has large negative Euler characteristic or is an n-punctured sphere visible in the diagram.

Mathematics

Physical Sciences

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Details

Title: Subtitle: Essential surfaces in highly twisted link complements
Creators: Ryan Blair - California State University, Long Beach
David Futer - Temple University
Maggy Tomova - University of Iowa
Resource Type: Journal article
Publication Details: Algebraic & geometric topology, Vol.15(3), pp.1501-1523
Publisher: GEOMETRY & TOPOLOGY PUBLICATIONS
DOI: 10.2140/agt.2015.15.1501
ISSN: 1472-2739
eISSN: 1472-2739
Number of pages: 23
Grant note: DMS-1007221; DMS-1408682; DMS-1054450 / NSF
Language: English
Date published: 01/01/2015
Academic Unit: Mathematics
Record Identifier: 9984240867202771

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