Systolic invariants of groups and 2 -complexes via Grushko decomposition

Yuli B. Rudyak[1]; Stéphane Sabourau[2]

  • [1] University of Florida Department of Mathematics PO Box 118105 Gainesville, FL 32611-8105 (USA)
  • [2] Université de Tours Laboratoire de Mathématiques et Physique Théorique CNRS UMR 6083 Fédération de recherche Dennis Poisson (FR 2964) Parc de Grandmont 37200 Tours (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 3, page 777-800
  • ISSN: 0373-0956

Abstract

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We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of  2 -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all 2 -complexes with unfree fundamental group that improves the previously known bounds in this dimension.

How to cite

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Rudyak, Yuli B., and Sabourau, Stéphane. "Systolic invariants of groups and $2$-complexes via Grushko decomposition." Annales de l’institut Fourier 58.3 (2008): 777-800. <http://eudml.org/doc/10334>.

@article{Rudyak2008,
abstract = {We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of $2$-complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all $2$-complexes with unfree fundamental group that improves the previously known bounds in this dimension.},
affiliation = {University of Florida Department of Mathematics PO Box 118105 Gainesville, FL 32611-8105 (USA); Université de Tours Laboratoire de Mathématiques et Physique Théorique CNRS UMR 6083 Fédération de recherche Dennis Poisson (FR 2964) Parc de Grandmont 37200 Tours (France)},
author = {Rudyak, Yuli B., Sabourau, Stéphane},
journal = {Annales de l’institut Fourier},
keywords = {Systole; systolic area; systolic ratio; $2$-complex; Grushko decomposition; systole; 2-complex},
language = {eng},
number = {3},
pages = {777-800},
publisher = {Association des Annales de l’institut Fourier},
title = {Systolic invariants of groups and $2$-complexes via Grushko decomposition},
url = {http://eudml.org/doc/10334},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Rudyak, Yuli B.
AU - Sabourau, Stéphane
TI - Systolic invariants of groups and $2$-complexes via Grushko decomposition
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 3
SP - 777
EP - 800
AB - We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of $2$-complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all $2$-complexes with unfree fundamental group that improves the previously known bounds in this dimension.
LA - eng
KW - Systole; systolic area; systolic ratio; $2$-complex; Grushko decomposition; systole; 2-complex
UR - http://eudml.org/doc/10334
ER -

References

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