Zero entropy and bounded topology

• Autores: Gabriel P. Paternain, Jimmy Petean
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 81, Nº 2, 2006, págs. 287-304
• Idioma: inglés
• DOI: 10.4171/cmh/53
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• Resumen

  • We study the existence of Riemannian metrics with zero topological entropy on a closed manifold $M$ with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to $M$ in such a way that the rank of the map induced in the pointed loop space homology grows exponentially. This result allows us to prove in dimensions four and five, that if $M$ admits a metric with zero entropy then its universal covering has the rational homotopy type of a finite elliptic CW complex. We conjecture that this is the case in every dimension