Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Comparing 2-handle additions to a genus 2 boundary component


Author: Scott A. Taylor
Journal: Trans. Amer. Math. Soc. 366 (2014), 3747-3769
MSC (2010): Primary 57M50
Published electronically: March 4, 2014
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one knots are prime and that genus is superadditive under a band sum. Additionally, we prove a collection of results comparing two 2-handle additions to a genus 2 boundary component of a compact, orientable 3-manifold. These results give a near complete solution to a conjecture of Scharlemann and provide evidence for a conjecture of Scharlemann and Wu. The proofs make use of a new theorem concerning the effects of attaching a 2-handle to a suture in the boundary of a sutured manifold.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 57M50

Retrieve articles in all journals with MSC (2010): 57M50


Additional Information

Scott A. Taylor
Affiliation: Department of Mathematics and Statistics, Colby College, Waterville, Maine 04901
Email: sataylor@colby.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06253-3
PII: S 0002-9947(2014)06253-3
Received by editor(s): November 3, 2011
Received by editor(s) in revised form: October 12, 2012
Published electronically: March 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.