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Volume distortion in homotopy groups
Manin, Fedor...

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Volume distortion in homotopy groups by Manin, Fedor ( Author )
Lemonjar Open Access
N.A
13-10-2014
Given a finite metric CW complex X and an element α∈πn(X), what are the properties of a geometrically optimal representative of α? We study the optimal volume of kα as a function of k. 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 X. 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 X in which all non-torsion homotopy classes are undistorted, that is, their distortion functions are linear.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1410.3368
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