The topology of the Banach–Mazur compactum

Antonyan, Sergey

Fundamenta Mathematicae, Tome 163 (2000), p. 209-232 / Harvested from The Polish Digital Mathematics Library

Résumé

Let J(n) be the hyperspace of all centrally symmetric compact convex bodies $A ⊆ \mathbb {R}^n$, n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let $J_0(n)$ be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) $J_0(2)/SO(2)$ is an Eilenberg-MacLane space $\mathbf {K}(\mathbb {Q},2)$; (4) $BM_0(2) = J_0(2)/O(2)$ is noncontractible; (5) BM(2) is a nonhomogeneous absolute retract. Other models for BM(n) are established.

Détail

Publié le : 2000-01-01

Zbl 0968.57022

EUDML-ID : urn:eudml:doc:212478

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