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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Deforming a PL submanifold of Euclidean space into a hyperplane


Author: Jože Vrabec
Journal: Trans. Amer. Math. Soc. 312 (1989), 155-178
MSC: Primary 57Q37; Secondary 57Q35
DOI: https://doi.org/10.1090/S0002-9947-1989-0937253-7
MathSciNet review: 937253
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Abstract: Let $ M$ be a closed, $ k$-connected, $ m$-dimensional $ {\text{PL}}$ submanifold of $ {\mathbb{R}^{2m - k - 1}}\;(1 \leq k \leq m - 4)$. The main result of this paper states that if $ m - k$ is even, then every embedding of $ M$ into $ {\mathbb{R}^{2m - k}}$ can be isotopically deformed into $ {\mathbb{R}^{2m - k - 1}}$, and specifies which embeddings of $ M$ into $ {\mathbb{R}^{2m - k}}$ can be deformed into $ {\mathbb{R}^{2m - k - 1}}$ in case $ m - k$ is odd.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0937253-7
Keywords: $ {\text{PL}}$ manifold, embedding, immersion, isotopy, concordance, Euclidean space, embedding space, suspension of disk embeddings
Article copyright: © Copyright 1989 American Mathematical Society