Daciberg Lima Gonçalves

TWISTED CONJUGACY CLASSES IN EXPONENTIAL GROWTH GROUPS

Let

Twisted conjugacy classes in nilpotent groups

\phi\,{:}\,G \to G

TWISTED CONJUGACY CLASSES IN WREATH PRODUCTS

be a group endomorphism where G is a finitely generated group of exponential growth, and denote by

The roots of the full twist for surface braid groups

R(\phi)

On the structure of surface pure braid groups

the number of twisted ϕ-conjugacy classes. Felshtyn and Hill ( K-theory 8 (1994) 367–393) conjectured that if ϕ is injective, then R(ϕ) is infinite. This paper shows that this conjecture does not hold in general. In fact, R(ϕ) can be finite for some automorphism ϕ. Furthermore, for a certain family of polycyclic groups, there is no injective endomorphism ϕ with

Homogeneous spaces in coincidence theory II

R({\phi}^n)\,{ for all n .

The lower central and derived series of the braid groups of the sphere

Abstract A group is said to have the R ∞ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R ∞ property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n ≧ 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R ∞ property. The R ∞ property for virtually abelian and for -nilpotent groups are also discussed.

Coincidence Reidemeister classes on nilmanifolds and nilpotent fibrations

Let G be a finitely generated abelian group and G ≀ ℤ be the wreath product. In this paper, we classify all such groups G for which every automorphism of G ≀ ℤ has infinitely many twisted conjugacy classes.

The coincidence Reidemeister classes of maps on nilmanifolds

Let

Self-coincidence of fibre maps

M