Minimal homeomorphisms and topological K-theory

0573356 - MÚ 2024 RIV CH eng J - Journal Article
Deeley, R. J. - Putnam, I. F. - Strung, Karen Ruth
Minimal homeomorphisms and topological K-theory.
Groups Geometry and Dynamics. Roč. 17, č. 2 (2023), s. 501-532. ISSN 1661-7207. E-ISSN 1661-7215
R&D Projects: GA ČR(CZ) GJ20-17488Y
EU Projects: European Commission(XE) 101119552 - CaLiForNIA
Institutional support: RVO:67985840
Keywords : minimal homeomorphisms * K-theory * classification of nuclear * C*-algebras
OECD category: Pure mathematics
Impact factor: 0.6, year: 2022
Method of publishing: Open access
https://doi.org/10.4171/ggd/707

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-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 K-theory or cohomol-ogy. In particular, although a non-zero Euler characteristic obstructs the existence of a minimal homeomorphism on a finite CW-complex, this is not the case on a compact metric space. We also allow for some control of the map on K-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 C-algebras will be discussed in another paper.
Permanent Link: https://hdl.handle.net/11104/0343818