2026-06-27T23:02:00Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/72352023-08-27T10:06:03Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Hernández Corbato, Luis
author
Nieves Rivera, David Jesús
author
Ruiz del Portal, Francisco R.
author
Sánchez Gabites, Jaime Jorge
2023-06-17T08:28:38Z
2023-06-17T08:28:38Z
2021
https://hdl.handle.net/20.500.14352/7235
The evaluation of Alexander-Spanier cochains over formal simplices in a topological space leads to a notion of integration of Alexander-Spanier cohomology classes over Cech homology classes. The integral defines an explicit and non-degenerate pairing between the Alexander-Spanier cohomology and the Cech homology. Instead of working on the limits that define both groups, most of the discussion is carried out "at scale U", for an open covering U. As an application, we generalize a result of Manning to arbitrary compact spaces X: we prove that the topological entropy of f : X → X is bounded from below by the logarithm of the spectral radius of the map induced in the first Cech cohomology group.
eng
Integration in Cech theories and a bound on entropy
journal article
URL
https://docta.ucm.es/bitstreams/702c8881-728a-4b58-b2a9-90067678a53d/download
File
MD5
eca6cf48fe1ebc6283a6304255f45fd1
626717
application/pdf
ruizdelportal_integration.pdf