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2019 Algebraic filling inequalities and cohomological width
Meru Alagalingam
Algebr. Geom. Topol. 19(6): 2855-2898 (2019). DOI: 10.2140/agt.2019.19.2855

Abstract

In his work on singularities, expanders and topology of maps, Gromov showed, using isoperimetric inequalities in graded algebras, that every real-valued map on the n–torus admits a fibre whose homological size is bounded below by some universal constant depending on n. He obtained similar estimates for maps with values in finite-dimensional complexes, by a Lusternik–Schnirelmann-type argument.

We describe a new homological filling technique which enables us to derive sharp lower bounds in these theorems in certain situations. This partly realises a programme envisaged by Gromov.

In contrast to previous approaches, our methods imply similar lower bounds for maps defined on products of higher-dimensional spheres.

Citation

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Meru Alagalingam. "Algebraic filling inequalities and cohomological width." Algebr. Geom. Topol. 19 (6) 2855 - 2898, 2019. https://doi.org/10.2140/agt.2019.19.2855

Information

Received: 25 October 2017; Revised: 16 February 2019; Accepted: 24 February 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142621
MathSciNet: MR4023331
Digital Object Identifier: 10.2140/agt.2019.19.2855

Subjects:
Primary: 55N05
Secondary: 55P62, 55S35

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 6 • 2019
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