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Abstract:
The TBFTf conjecture, which is a modification of a conjecture by Fel’shtyn and Hill, says that
if the Reidemeister number R(φ) of an automorphism φ of a (countable discrete) group G is finite, then it
coincides with the number of fixed points of the corresponding homeomorphism φˆ of Gˆf (the part of the
unitary dual formed by finite-dimensional representations). The study of this problem for residually finite
groups has been the subject of some recent activity. We prove here that for infinitely generated residually
finite groups there are positive and negative examples for this conjecture. It is detected that the finiteness
properties of the number of fixed points of φ itself also differ from the finitely generated case.