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A MATROID PROPERTY OF FILLING CURVES

Part of: Low-dimensional topology

Published online by Cambridge University Press:  21 July 2025

INGRID IRMER Open the ORCID record for INGRID IRMER [Opens in a new window]
INGRID IRMER*
Affiliation:
SUSTech International Center for Mathematics, and Department of Mathematics, https://ror.org/049tv2d57 Southern University of Science and Technology , Shenzhen, PR China
*
e-mail: ingridmary@sustech.edu.cn
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Abstract

A subset of a finite set of filling curves on a surface is not necessarily filling. However, when a filling set spans homology and curves intersect pairwise at most once, it is shown that one can always add a curve and subtract a different curve to obtain a filling set that spans homology. A motivation for filling sets of curves that span homology comes from the Thurston spine and the Steinberg module of the mapping class group.

Keywords

Steinberg moduleThurston spinemapping class groupsystole

MSC classification

Secondary: 57M60: Group actions in low dimensions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 5
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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