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Fixed point theory and the K-theoretic trace

Ross Geoghegan, Andrew Nicas (1999)

Banach Center Publications

The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus K 0 ) and 1-parameter fixed point theory (versus K 1 ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.

Fixed point theory for homogeneous spaces, II

Peter Wong (2005)

Fundamenta Mathematicae

Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously known under...

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