Geodesic
Algebraic filling inequalities and cohomological width
Alagalingam, Meru1
1 Universität Augsburg, Augsburg, Germany
Algebraic and Geometric Topology, Tome 19 (2019) no. 6, pp. 2855-2898

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.2855
Classification : 55N05, 55P62, 55S35
Keywords: waist inequalities, space of cycles, filling inequalities, cohomological complexity, tori, essential manifolds, rational homotopy theory

Alagalingam, Meru 1

1 Universität Augsburg, Augsburg, Germany 
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Alagalingam, Meru. Algebraic filling inequalities and cohomological width. Algebraic and Geometric Topology, Tome 19 (2019) no. 6, pp. 2855-2898. doi: 10.2140/agt.2019.19.2855

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