Systolic freedom of loop space

Mikhail G. Katz; Alexander I. Suciu

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Systolic freedom of loop space

Mikhail G. Katz·Alexander I. Suciu

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Abstract

Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case of a pair of complementary dimensions, for which a direct geometric construction works and gives the analogous theorem in complete generality. In the present paper, we use Sullivan's telescope model for the rationalisation of a space to observe systolic freedom.

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Mikhail G. Katz, Alexander I. Suciu. 2001-06-19. Systolic freedom of loop space. https://arxiv.org/abs/math/0106153

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