Systolic almost-rigidity modulo 2

Hannah Alpert; Alexey Balitskiy; Larry Guth

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arXiv · 2206.01968

Systolic almost-rigidity modulo 2

Hannah Alpert·Alexey Balitskiy·Larry Guth

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Abstract

No power law systolic freedom is possible for the product of mod $2$ systoles of dimension $1$ and codimension $1$. This means that any closed $n$-dimensional Riemannian manifold $M$ of bounded local geometry obeys the following systolic inequality: the product of its mod $2$ systoles of dimensions $1$ and $n-1$ is bounded from above by $c(n,\varepsilon) \mbox{Vol}(M)^{1+\varepsilon}$, if finite (if $H_1(M; \mathbb{Z}/2)$ is non-trivial).

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Hannah Alpert, Alexey Balitskiy, Larry Guth. 2022-06-04. Systolic almost-rigidity modulo 2. https://arxiv.org/abs/2206.01968

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