A Zp-index homomorphism for Zp-spaces

• Autores: Pedro L. Q. Pergher
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 305-314
• Idioma: inglés
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• Resumen

  • Let Zp be the cyclic group of order p and let (X,T) be a Zp-space, that is, a topological space X equipped with a free action of Zp, generated by a periodic homeomorphism T of X with period p. In this paper we construct a Zp-index graded homomorphism associated with (X,T), defined on the equivariant homology Zp-modules of (X,T) and with values in Zp. Using this Zp-index homomorphism we prove that, if (X,T) and (Y,S) are Zp-spaces and p=2q with q odd, then, under certain homological conditions on X and Y, there is no equivariant map from (X,T) into (Y,S). This result includes the particular situation in which the target spaces (Y,S) are spheres of odd dimension, equipped with the standard free periodic homeomorphism of period p. This is a special case of a previous result of T. Kobayashi, which handled this case with no restriction on p.