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

Access to Document

10.1112/blms/bdm031

Cite this

@article{08cdb6e43d6544709cd4a727df7d5f77,

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.",

author = "Akhmet'Ev, \{Pyotr M.\} and Eccles, \{Peter J.\}",

year = "2007",

month = jun,

doi = "10.1112/blms/bdm031",

language = "English",

volume = "39",

pages = "473--481",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley \& Sons Ltd",

number = "3",

}

TY - JOUR

T1 - The relationship between framed bordism and skew-framed bordism

AU - Akhmet'Ev, Pyotr M.

AU - Eccles, Peter J.

PY - 2007/6

Y1 - 2007/6

N2 - 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.

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.

U2 - 10.1112/blms/bdm031

DO - 10.1112/blms/bdm031

M3 - Article

SN - 0024-6093

VL - 39

SP - 473

EP - 481

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 3

ER -

The relationship between framed bordism and skew-framed bordism

Abstract

Access to Document

Fingerprint

Cite this