| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Katholieke Univ Leuven, Campus Kulak Kortrijk, E Sabbelaan 53, B-8500 Kortrijk - Belgium
[2] Univ Sao Paulo, Dept Matemat IME, Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE LONDON MATHEMATICAL SOCIETY; v. 3, n. 1, p. 28-45, 2016. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 12/24454-8 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |