8,987 research outputs found
General removal lemma
We formulate and prove a general result in spirit of hypergraph removal lemma
for measurable functions of several variables.Comment: 5 page
Volume distortion in homotopy groups
Given a finite metric CW complex and an element ,
what are the properties of a geometrically optimal representative of ?
We study the optimal volume of as a function of . Asymptotically,
this function, whose inverse, for reasons of tradition, we call the volume
distortion, turns out to be an invariant with respect to the rational homotopy
of . We provide a number of examples and techniques for studying this
invariant, with a special focus on spaces with few rational homotopy groups.
Our main theorem characterizes those in which all non-torsion homotopy
classes are undistorted, that is, their distortion functions are linear.Comment: 49 pages, 4 figures. Accepted for publication in Geometric and
Functional Analysis (GAFA
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