Reidemeister torsion and integrable Hamiltonian systems.
Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
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.
Nielsen number is a knot invariant
We show that the Nielsen number is a knot invariant via representation variety.
Nielsen fixed point theory and symplectic Floer homology
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion
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...
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