The R-infinity property for nilpotent quotients of surface groups

Autor(es)

Dekimpe, Karel ^[1] ; Goncalves, Daciberg L. ^[2]

Afiliação do(s) autor(es)

^[1] Katholieke Univ Leuven, Campus Kulak Kortrijk, E Sabbelaan 53, B-8500 Kortrijk - Belgium

^[2] Univ Sao Paulo, Dept Matemat IME, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE LONDON MATHEMATICAL SOCIETY; v. 3, n. 1, p. 28-45, 2016.
• Citações Web of Science: 2

Resumo

A group G is said to have the R-infinity property if, for any automorphism phi of G, the number R(phi) of twisted conjugacy classes (or Reidemeister classes) is infinite. It is well known that when G is the fundamental group of a closed surface of negative Euler characteristic, it has the R-infinity property. In this work, we compute the least integer c, called the R-infinity-nilpotency degree of G, such that the group G/gamma(c+1)(G) has the R-infinity property, where gamma(r)(G) is the rth term of the lower central series of G. We show that c = 4 for G the fundamental group of any orientable closed surface S-g of genus g > 1. For the fundamental group of the non-orientable surface N-g (the connected sum of g projective planes) this number is 2(g - 1) (when g > 2). A similar concept is introduced using the derived series G((r)) of a group G. Namely, the R-infinity-solvability degree of G, which is the least integer c such that the group G/G((c)) has the R-infinity property. We show that the fundamental group of an orientable closed surface S-g has R-infinity-solvability degree 2. As a by-product of our research, we find a lot of new examples of nilmanifolds on which every self-homotopy equivalence can be deformed into a fixed point free map. (AU)

• Processo FAPESP: 12/24454-8 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático