Embeddings of Z(2)-homology 3-spheres in R-5 up to regular homotopy

Authors
Takase, M
Citation
M. Takase, Embeddings of Z(2)-homology 3-spheres in R-5 up to regular homotopy, PAC J MATH, 193(1), 2000, pp. 249-256
Citations number
9
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
193
Issue
1
Year of publication
2000
Pages
249 - 256
Database
ISI
SICI code
0030-8730(200003)193:1<249:EOZ3IR>2.0.ZU;2-T
Abstract
Let F : M3 --> R-5 be an embedding of an (oriented) Z(2)-homology 3-sphere M-3 in R-5. Then F bounds an embedding of an oriented manifold W-4 in R-5. It is well known that the signature sigma(W-4) of W-4 is equal to the mu-in variant of M-3 modulo 16. In this paper we prove that sigma(W-4) itself com pletely determines the regular homotopy class of F.