A remark on the action of the mapping class group on the unit tangent bundle

J. Souto[1]

  • [1] Department of Mathematics, University of Michigan, Ann Arbor

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 3-4, page 589-601
  • ISSN: 0240-2963

Abstract

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We prove that the standard action of the mapping class group Map ( Σ ) of a surface Σ of sufficiently large genus on the unit tangent bundle T 1 Σ is not homotopic to any smooth action.

How to cite

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Souto, J.. "A remark on the action of the mapping class group on the unit tangent bundle." Annales de la faculté des sciences de Toulouse Mathématiques 19.3-4 (2010): 589-601. <http://eudml.org/doc/115866>.

@article{Souto2010,
abstract = {We prove that the standard action of the mapping class group $\{\rm Map\}(\Sigma )$ of a surface $\Sigma $ of sufficiently large genus on the unit tangent bundle $T^1\Sigma $ is not homotopic to any smooth action.},
affiliation = {Department of Mathematics, University of Michigan, Ann Arbor},
author = {Souto, J.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {mapping class group; Nielsen realization problem},
language = {eng},
number = {3-4},
pages = {589-601},
publisher = {Université Paul Sabatier, Toulouse},
title = {A remark on the action of the mapping class group on the unit tangent bundle},
url = {http://eudml.org/doc/115866},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Souto, J.
TI - A remark on the action of the mapping class group on the unit tangent bundle
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2010
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 3-4
SP - 589
EP - 601
AB - We prove that the standard action of the mapping class group ${\rm Map}(\Sigma )$ of a surface $\Sigma $ of sufficiently large genus on the unit tangent bundle $T^1\Sigma $ is not homotopic to any smooth action.
LA - eng
KW - mapping class group; Nielsen realization problem
UR - http://eudml.org/doc/115866
ER -

References

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  15. Parwani (K.).— C 1 actions on the mapping class groups on the circle, Algebr. Geom. Topol. 8 (2008). Zbl1155.37028MR2443102
  16. Powell (J.).— Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978). Zbl0391.57009MR494115
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