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Classification of trisections and the Generalized Property R Conjecture


Authors: Jeffrey Meier, Trent Schirmer and Alexander Zupan
Journal: Proc. Amer. Math. Soc. 144 (2016), 4983-4997
MSC (2010): Primary 57M25, 57M99, 57Q25
Published electronically: May 24, 2016
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Abstract: We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a stable version of the Generalized Property R Conjecture for $ c$-component links with tunnel number at most $ c$.


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Additional Information

Jeffrey Meier
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47408
Email: jlmeier@indiana.edu

Trent Schirmer
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: trent.schirmer@okstate.edu

Alexander Zupan
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska, 68588
Email: zupan@unl.edu

DOI: https://doi.org/10.1090/proc/13105
Received by editor(s): March 30, 2015
Received by editor(s) in revised form: August 6, 2015, and January 14, 2016
Published electronically: May 24, 2016
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2016 American Mathematical Society