Spin structures and codimension two embeddings of 3-manifolds up to regular homotopy

Osamu Saeki, Masamichi Takase

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We clarify the structure of the set of regular homotopy classes containing embeddings of a 3-manifold into 5-space inside the set of all regular homotopy classes of immersions with trivial normal bundles. As a consequence, we show that for a large class of 3-manifolds M 3 , the following phenomenon occurs: there exists a codimension two immersion of the 3-sphere whose double points cannot be eliminated by regular homotopy, but can be eliminated after taking the connected sum with a codimension two embedding of M 3 . This involves introducing and studying an equivalence relation on the set of spin structures on M 3 . Their associated μ-invariants also play an important role.

Original languageEnglish
Pages (from-to)5049-5061
Number of pages13
JournalTransactions of the American Mathematical Society
Volume354
Issue number12
DOIs
Publication statusPublished - Dec 1 2002
Externally publishedYes

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Spin Structure
Homotopy
Codimension
Immersion
Connected Sum
Normal Bundle
Equivalence relation
Trivial
Invariant
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Spin structures and codimension two embeddings of 3-manifolds up to regular homotopy. / Saeki, Osamu; Takase, Masamichi.

In: Transactions of the American Mathematical Society, Vol. 354, No. 12, 01.12.2002, p. 5049-5061.

Research output: Contribution to journalArticle

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