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Algebraic filling
inequalities and cohomological width
Meru Alagalingam |
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Algebraic & Geometric Topology 19 (2019) 2855–2898
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Abstract |
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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 –torus admits a fibre whose homological size is bounded below by some universal constant depending on . 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. |
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Keywords
waist inequalities, space of cycles, filling inequalities,
cohomological complexity, tori, essential manifolds,
rational homotopy theory
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Mathematical Subject Classification 2010
Primary: 55N05
Secondary: 55P62, 55S35
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References |
Publication
Received: 25 October 2017
Revised: 16 February 2019
Accepted: 24 February 2019
Published: 20 October 2019
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Authors |
| Meru Alagalingam | |
| Universität Augsburg Augsburg Germany |
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