Osaka Journal of Mathematics

Order of the canonical vector bundle over configuration spaces of projective spaces

Shiquan Ren

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Abstract

The order of a vector bundle is the smallest positive integer $n$ such that the vector bundle's $n$-fold self-Whitney sum is trivial. Since 1970's, the order of the canonical vector bundle over configuration spaces of Euclidean spaces has been studied by F.R. Cohen, R.L. Cohen, N.J. Kuhn and J.L. Neisendorfer [4], F.R. Cohen, M.E. Mahowald and R.J. Milgram [6], and S.W. Yang [17, 18]. And the order of the canonical vector bundle over configuration spaces of closed orientable Riemann surfaces with genus greater than or equal to one has been studied by F.R. Cohen, R.L. Cohen, B. Mann and R.J. Milgram [5]. In this paper, we study the order of the canonical vector bundle over configuration spaces of projective spaces as well as of the Cartesian products of a projective space and a Euclidean space.

Article information

Source
Osaka J. Math. Volume 54, Number 4 (2017), 623-634.

Dates
First available in Project Euclid: 20 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1508486563

Zentralblatt MATH identifier
06821127

Subjects
Primary: 55R80: Discriminantal varieties, configuration spaces 55R10: Fiber bundles
Secondary: 55P15: Classification of homotopy type 55P40: Suspensions

Citation

Ren, Shiquan. Order of the canonical vector bundle over configuration spaces of projective spaces. Osaka J. Math. 54 (2017), no. 4, 623--634.https://projecteuclid.org/euclid.ojm/1508486563


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