0573356 - MÚ 2024 RIV CH eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GJ20-17488Y
GRANT EU: European Commission(XE) 101119552 - CaLiForNIA
Institucionální podpora: RVO:67985840
Klíčová slova: minimal homeomorphisms * K-theory * classification of nuclear * C*-algebras
Obor OECD: Pure mathematics
Impakt faktor: 0.6, rok: 2022
Způsob publikování: 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.
Trvalý link: https://hdl.handle.net/11104/0343818