Arc distance equals level number

Authors:
Sangbum Cho, Darryl McCullough and Arim Seo

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2801-2807

MSC (2000):
Primary 57M25

Published electronically:
March 18, 2009

MathSciNet review:
2497495

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a knot in -bridge position with respect to a genus- Heegaard surface that splits a -manifold into two handlebodies and . One can move by isotopy keeping in and in so that lies in a union of parallel genus- surfaces tubed together by straight tubes, and intersects each tube in two arcs connecting the ends. We prove that the minimum for which this is possible is equal to a Hempel-type distance invariant defined using the arc complex of the two-holed genus- surface.

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Additional Information

**Sangbum Cho**

Affiliation:
Department of Mathematics, University of California, Riverside, California 92521

Email:
scho@math.ucr.edu

**Darryl McCullough**

Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Email:
dmccullough@math.ou.edu

**Arim Seo**

Affiliation:
Department of Mathematics, California State University, San Bernardino, California 92407

Email:
aseo@csusb.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-09-09874-8

Received by editor(s):
September 22, 2008

Received by editor(s) in revised form:
January 7, 2009

Published electronically:
March 18, 2009

Additional Notes:
The second author was supported in part by NSF grant DMS-0802424

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.