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1
Content available remote

Nielsen number is a knot invariant

100%
Fel'shtyn A.
Banach Center Publications
|
2007
|
tom 77
|
nr 1
69-74
EN
We show that the Nielsen number is a knot invariant via representation variety.
2
Content available remote

Nielsen fixed point theory and symplectic Floer homology

100%
Fel'shtyn A.
Banach Center Publications
|
2007
|
tom 77
|
nr 1
75-87
EN
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
3
Content available remote

Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

100%
Fel'shtyn A.
Banach Center Publications
|
2009
|
tom 85
|
nr 1
31-42
EN
It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.
4
Content available remote

Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

63%
Alexander Fel'shtyn, Hill R.
Banach Center Publications
|
1999
|
tom 49
|
nr 1
77-116
EN
In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a finite group and a finitely generated free Abelian group with the Lefschetz zeta function of the unitary dual map, and as a consequence obtain a connection of the Reidemeister zeta function with Reidemeister torsion. We also prove congruences for Reidemeister numbers which are the same as those found by Dold for Lefschetz numbers.
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