Equivariant Nielsen invariants for discrete groups

• Autores: Julia Weber
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 231, Nº 1, 2007, pág. 239
• Idioma: inglés
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• Resumen

  • For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f : X ? X. Under mild hypotheses, these lower bounds are sharp.

    We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic to a fixed point free G-map if the generalized equivariant Lefschetz invariant ?G(f) is zero. Finally, we prove a converse of the equivariant Lefschetz fixed point theorem.