Journal article
Small filling sets of curves on a surface
- Abstract:
- We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus g which fill and pairwise intersect at most K≥1 times is 2√g / √K as g→ ∞. We then bound from below the cardinality of a filling set of systoles by g / log(g). This illustrates that the topological condition that a set of curves pairwise intersect at most once is quite far from the geometric condition that such a set of curves can arise as systoles.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Author's original, pdf, 207.4KB, Terms of use)
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- Publisher copy:
- 10.1016/j.topol.2010.10.007
Authors
+ Engineering and Physical Sciences Research Council ; National Science Foundation
More from this funder
- Funding agency for:
- Pettet, A
- Grant:
- EP/F003897
- DMS-0856143
- DMS-0602191
- Publisher:
- Elsevier
- Journal:
- Topology and its Applications More from this journal
- Volume:
- 158
- Issue:
- 1
- Pages:
- 84–92
- Publication date:
- 2011-01-01
- Edition:
- Author's Original
- DOI:
- ISSN:
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0166-8641
- Language:
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English
- Keywords:
- Subjects:
- UUID:
-
uuid:e4891600-f09c-4504-a925-f2d0578492b9
- Local pid:
-
ora:10779
- Deposit date:
-
2015-03-31
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 2010
- Notes:
- Copyright 2010 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
- Licence:
- Other
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