Journal article

### An upper bound on the revised first Betti number and a torus stability result for RCD spaces

Abstract:

We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact $RCD^{*}(K,N)$ space, in the same spirit of the celebrated Gromov-Gallot upper bound on the first Betti number for a smooth compact Riemannian manifold with Ricci curvature bounded below. When the synthetic lower Ricci bound is close enough to (negative) zero and the aforementioned upper bound on the revised first Betti number is saturated (i.e. equal to the inte...

Publication status:
Accepted
Peer review status:
Peer reviewed

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
EMS Press Publisher's website
Journal:
Commentarii Mathematici Helvetici Journal website
Acceptance date:
2022-02-06
EISSN:
1420-8946
ISSN:
0010-2571
Language:
English
Keywords:
Pubs id:
1171911
Local pid:
pubs:1171911
Deposit date:
2022-02-07

### Terms of use

#### Views and Downloads

If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP