Universität zu Köln

Lytchak, Alexander and Nagano, Koichi (2022). Topological regularity of spaces with an upper curvature bound. J. Eur. Math. Soc., 24 (1). S. 137 - 166. BERLIN: EUROPEAN MATHEMATICAL SOC-EMS. ISSN 1435-9855

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Abstract

We prove that a locally compact space with an upper curvature bound is a topological manifold if and only if all of its spaces of directions are homotopy equivalent and not contractible. We discuss applications to homology manifolds, limits of Riemannian manifolds and deduce a sphere theorem.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Nagano, Koichi UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-667803
DOI:	10.4171/JEMS/1091
Journal or Publication Title:	J. Eur. Math. Soc.
Volume:	24
Number:	1
Page Range:	S. 137 - 166
Date:	2022
Publisher:	EUROPEAN MATHEMATICAL SOC-EMS
Place of Publication:	BERLIN
ISSN:	1435-9855
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language APPROXIMATING HOMOTOPY-EQUIVALENCES; FINITENESS THEOREMS; LOCAL-STRUCTURE; SPHERE THEOREM; HOMOLOGY; MANIFOLDS Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66780