arXiv subjects

Guillaume Bulteau

Publications and source records attributed to Guillaume Bulteau.

3 recordsLinked to original sources

arXiv2017

Systolic geometry and simplicial complexity for groups

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 {\it 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.

math.GT↗

arXiv2015

Regular geometric cycles

Let $π$ be a finitely presented group. If h is a non trivial homology class in Hn($π$; Z), a theorem of Gromov (see [Gro83], 6) asserts the existence of regular geometric cycles which represent h, whose relative systolic volume is as close as desired to the systolic volume of h, in which we can control the volume of balls of radius less than half of the cycle's relative systol. The aim of this note is to explain and provide a complete proof of this result.

math.GT↗

arXiv2015

Systolic geometry and regularization technique

The aim of this text is to present the concept of systole of a compact riemannian manifold and to give an overview of systolic geometry. I will also present the "regularization technique", which leads to major results in systolic geometry. I will detail how this technique allows to link the systolic volume of some closed riemannian manifolds to homotopical invariants of these manifolds, such as the Betti numbers (according to Gromov) and the minimal entropy (according to Sabourau).

math.GT↗