An end theorem for stratified spaces | Zendy

Frank Connolly | Zendy; Bogdan Vajiac | Zendy

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An end theorem for stratified spaces

Author(s) -

Frank Connolly,

Bogdan Vajiac

Publication year - 1999

Publication title -

inventiones mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.536

H-Index - 125

eISSN - 1432-1297

pISSN - 0020-9910

DOI - 10.1007/s002220050294

Subject(s) - mathematics , manifold (fluid mechanics) , boundary (topology) , closed manifold , pure mathematics , mathematical analysis , transversality , space (punctuation) , invariant manifold , mechanical engineering , linguistics , philosophy , engineering

We show that a tame ended stratied space X is the interior of a compact stratied space if and only if a K-theoretic obstruction (X) vanishes. The obstruction (X) is a localization of Quinn's mapping cylinder neighborhood obstruction. The main results are Theorem 1.6 and Theorem 1.7 below. In particular, this explains when a G-manifold is the interior of a compact G-manifold with boundary. Our methods include a new transversality theorem, Corollary 1.17.

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