Minimal homeomorphisms and topological -theory

  • Robin J. Deeley

    University of Colorado, Boulder, USA
  • Ian F. Putnam

    University of Victoria, Canada
  • Karen R. Strung

    Czech Academy of Sciences, Prague, Czechia
Minimal homeomorphisms and topological $K$-theory cover
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The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite -complexes. We show that these obstructions do not hold for more general spaces. Minimal homeomorphisms are constructed on compact connected metric spaces with any prescribed finitely generated -theory or cohomology. In particular, although a non-zero Euler characteristic obstructs the existence of a minimal homeomorphism on a finite -complex, this is not the case on a compact metric space. We also allow for some control of the map on -theory and cohomology induced from these minimal homeomorphisms. This allows for the construction of many minimal homeomorphisms that are not homotopic to the identity. Applications to -algebras will be discussed in another paper.

Cite this article

Robin J. Deeley, Ian F. Putnam, Karen R. Strung, Minimal homeomorphisms and topological -theory. Groups Geom. Dyn. 17 (2023), no. 2, pp. 501–532

DOI 10.4171/GGD/707