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Embeddings of polyhedra in Rm and the deleted product obstruction

✍ Scribed by J. Segal; A. Skopenkov; S. Spiez

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 715 KB
Volume: 85
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00157-0

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✦ Synopsis

Weber has proved that if 2m 3 3(n + 1) then an n-dimensional polyhedron K embeds in Iw" if and only if there exists an equivariant map from the deleted product K* into the sphere Y-'.

As a consequence he has obtained that in the same range of dimensions an n-dimensional polyhedron embeds in I?? if and only if it quasi embeds in Iw". We show that for m > max(4, n) the dimension restrictions in Weber's results are necessary in all cases. This leaves only two open cases remaining (namely m = 3 and n = 2 or 3) in related questions about embeddings.

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