Peter Wong

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

Reidemeister numbers of equivariant maps

R(\phi)

Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps

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 .

Wecken property for roots

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.

A relative generalized Lefschetz number

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.

Twisted Conjugacy for Virtually Cyclic Groups and Crystallographic Groups

In this paper, we generalize the arithmetic congruence relations among the Reidemeister numbers of iterates of maps to similar congruences for equivariant maps.

Fixed Point Theory for Homogeneous Spaces A Brief Survey

Abstract In this paper we generalize well known product formulae for the Nielsen number of a fibre preserving map, to give addition formulae for such maps. We give necessary and sufficient conditions for when a naive addition formula expressing the Nielsen number of the fibre map as a simple sum of Nielsen numbers on the fibres is valid. In the second part of the paper we extend to the nonorientable situation the definition and properties of a Nielsen type number of a fibre preserving map introduced by the first author.