On the Betti number of the space of invariant paths on the space whose cohomology is the exterior algebra with two generators
type: Item
instance of: scholarly article
title: On the Betti number of the space of invariant paths on the space whose cohomology is the exterior algebra with two generators
zbMATH Open document ID: 1020.55003
DOI: 10.1016/S0166-8641(01)00266-8
author: Katsuhiko Kuribayashi
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Let \(M\) a Riemannian closed manifold whose \(\text{mod 2}\) cohomology algebra is isomorphic to that of the product of two spheres with different dimensions. Using the Cobar type Eilenberg-Moore spectral sequence, the author proves that every isometry on \(M\) has infinitely many invariant geodesics. This result is obtained from a good characterization for the boundeness of rational Betti numbers of the space of invariant paths in \(M\).
Mathematics Subject Classification ID: 55T20
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 53C99
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 57T35
zbMATH DE Number: 1879116
zbMATH Keywords: closed geodesic
zbMATH Keywords: cobar type Eilenberg-Moore spectral sequences
zbMATH Keywords: isometry invariant geodesics
zbMATH Keywords: space of invariant paths
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879116