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.
PDF Access Denied
We have not been able to recognize your IP address
44.201.199.251
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.