Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic filling inequalities and cohomological width   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
realizes 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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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an