Margulis Lemma, entropy and free products

Filippo Cerocchi[1]

  • [1] Università di Roma “Sapienza” Dipartimento di Matematica “G. Castelnuovo” Piazzale Aldo Moro 5 00185 Roma (Italy) & Université Grenoble 1 Institut Fourier 100 rue des maths BP 74 38402 St. Martin d’Hères (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1011-1030
  • ISSN: 0373-0956

Abstract

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We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product A * B , without 2-torsion. Moreover, if A * B is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.

How to cite

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Cerocchi, Filippo. "Margulis Lemma, entropy and free products." Annales de l’institut Fourier 64.3 (2014): 1011-1030. <http://eudml.org/doc/275569>.

@article{Cerocchi2014,
abstract = {We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product $A*B$, without 2-torsion. Moreover, if $A* B$ is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.},
affiliation = {Università di Roma “Sapienza” Dipartimento di Matematica “G. Castelnuovo” Piazzale Aldo Moro 5 00185 Roma (Italy) & Université Grenoble 1 Institut Fourier 100 rue des maths BP 74 38402 St. Martin d’Hères (France)},
author = {Cerocchi, Filippo},
journal = {Annales de l’institut Fourier},
keywords = {Entropy; growth of groups; free products; systole; entropy},
language = {eng},
number = {3},
pages = {1011-1030},
publisher = {Association des Annales de l’institut Fourier},
title = {Margulis Lemma, entropy and free products},
url = {http://eudml.org/doc/275569},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Cerocchi, Filippo
TI - Margulis Lemma, entropy and free products
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1011
EP - 1030
AB - We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product $A*B$, without 2-torsion. Moreover, if $A* B$ is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.
LA - eng
KW - Entropy; growth of groups; free products; systole; entropy
UR - http://eudml.org/doc/275569
ER -

References

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  12. G. Robert, Invariants topologiques et géométriques reliés aux longuers des géodésiques et aux sections harmoniques de fibrés, (1994) 
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