Abstract
Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 10-01-00257-a
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: Finsler-12-BS01-0009-02
Funding statement: This work was partially supported by the grant RFSF 10-01-00257-a and the program ANR Finsler-12-BS01-0009-02.
Acknowledgements
The authors are grateful to the referees whose valuable comments lead us to considerably improve the presentation of this article, and also to one of the referees who pointed out a mistake in the initial proof of Theorem 1.2.
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