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Arc distance equals level number
Author(s):
Sangbum
Cho;
Darryl
McCullough;
Arim
Seo
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2801-2807.
MSC (2000):
Primary 57M25
Posted:
March 18, 2009
MathSciNet review:
2497495
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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.
References:
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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:
10.1090/S0002-9939-09-09874-8
PII:
S 0002-9939(09)09874-8
Received by editor(s):
September 22, 2008,
Received by editor(s) in revised form:
January 7, 2009
Posted:
March 18, 2009
Additional Notes:
The second author was supported in part by NSF grant DMS-0802424
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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