The relationship between framed bordism and skew-framed bordism

Pyotr M. Akhmet'Ev; Peter J. Eccles

doi:10.1112/blms/bdm031

The relationship between framed bordism and skew-framed bordism

Pyotr M. Akhmet'Ev, Peter J. Eccles

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we show that each stably parallelizable manifold can be immersed in some Euclidean space so that it is a skew-framed boundary, and can be immersed in some Euclidean space so that it is framed bordant to the double cover of a skew-framed manifold. These results are simple consequences of the Kahn-Priddy theorem and James periodicity. © 2007 London Mathematical Society.

Original language	English
Pages (from-to)	473-481
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	3
DOIs	https://doi.org/10.1112/blms/bdm031
Publication status	Published - Jun 2007

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title = "The relationship between framed bordism and skew-framed bordism",

abstract = "In this paper we show that each stably parallelizable manifold can be immersed in some Euclidean space so that it is a skew-framed boundary, and can be immersed in some Euclidean space so that it is framed bordant to the double cover of a skew-framed manifold. These results are simple consequences of the Kahn-Priddy theorem and James periodicity. {\textcopyright} 2007 London Mathematical Society.",

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AB - In this paper we show that each stably parallelizable manifold can be immersed in some Euclidean space so that it is a skew-framed boundary, and can be immersed in some Euclidean space so that it is framed bordant to the double cover of a skew-framed manifold. These results are simple consequences of the Kahn-Priddy theorem and James periodicity. © 2007 London Mathematical Society.

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DO - 10.1112/blms/bdm031

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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The relationship between framed bordism and skew-framed bordism

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