Voir la notice de l'article provenant de la source Annals of Mathematics website
We show that a closed, connected and orientable Riemannian manifold $M$ of dimension $d$ that admits a nonconstant quasiregular mapping from $\mathbb {R}^d$ must have bounded dimension of the cohomology independent of the distortion of the map. The dimension of the degree $l$ de Rham cohomology of $M$ is bounded above by $\binom {d}{l}$. This is a sharp upper bound that proves the Bonk-Heinonen conjecture. A corollary of this theorem answers an open problem posed by Gromov in 1981. He asked whether there exists a \hbox $d$-dimensional, simply connected manifold that does not admit a quasiregular mapping from $\mathbb {R}^d$. Our result gives an affirmative answer to this question.
@article{10_4007_annals_2019_189_3_5,
author = {Eden Prywes},
title = {A bound on the cohomology of quasiregularly elliptic manifolds},
journal = {Annals of mathematics},
pages = {863--883},
publisher = {mathdoc},
volume = {189},
number = {3},
year = {2019},
doi = {10.4007/annals.2019.189.3.5},
mrnumber = {3961085},
zbl = {07097492},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.5/}
}
TY - JOUR AU - Eden Prywes TI - A bound on the cohomology of quasiregularly elliptic manifolds JO - Annals of mathematics PY - 2019 SP - 863 EP - 883 VL - 189 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.5/ DO - 10.4007/annals.2019.189.3.5 LA - en ID - 10_4007_annals_2019_189_3_5 ER -
%0 Journal Article %A Eden Prywes %T A bound on the cohomology of quasiregularly elliptic manifolds %J Annals of mathematics %D 2019 %P 863-883 %V 189 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.5/ %R 10.4007/annals.2019.189.3.5 %G en %F 10_4007_annals_2019_189_3_5
Eden Prywes. A bound on the cohomology of quasiregularly elliptic manifolds. Annals of mathematics, Tome 189 (2019) no. 3, pp. 863-883. doi: 10.4007/annals.2019.189.3.5
Cité par Sources :