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EXHAUSTION OF THE CURVE GRAPH VIA RIGID EXPANSIONS

Part of: Low-dimensional topology Special aspects of infinite or finite groups

Published online by Cambridge University Press:  06 July 2018

JESÚS HERNÁNDEZ HERNÁNDEZ
JESÚS HERNÁNDEZ HERNÁNDEZ*
Affiliation:
Centro de Ciencias Matemáticas, UNAM, Campus Morelia, Morelia, Mich. 58190, Mexico e-mail: jhdezhdez@gmail.com, https://sites.google.com/site/jhdezhdez/
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Abstract

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For an orientable surface S of finite topological type with genus g ≥ 3, we construct a finite set of curves whose union of iterated rigid expansions is the curve graph $\mathcal{C}$(S). The set constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid set in Aramayona and Leininger, J. Topology Anal.5(2) (2013), 183–203 and Aramayona and Leininger, Pac. J. Math.282(2) (2016), 257–283, and in fact a consequence of our proof is that Aramayona and Leininger's set also exhausts the curve graph via rigid expansions.

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 57M07: Topological methods in group theory

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 195 - 230
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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