Year: 2021
Type: article
Abstract: We show that if a compact, connected, and oriented nmanifold M without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the real singular cohomology ring H * (M ; R) of M is bounded from above by 2 n .This is a positive answer to a dynamical counterpart of the Bonk-Heinonen conjecture on the cohomology bound for quasiregularly elliptic manifolds.The proof is based on an intermediary result that, if M is not a rational homology sphere, then each such uniformly quasiregular self-map on M has a Julia set of positive Lebesgue measure.
Source: American Journal of Mathematics
Author: Ilmari Kangasniemi
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Helsingin Yliopisto
OpenAlex ID: W2773047756