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# Mathematics > Algebraic Topology

# Title: Order of the canonical vector bundle over configuration spaces of disjoint unions of spheres

(Submitted on 16 May 2016 (v1), last revised 4 Apr 2018 (this version, v4))

Abstract: Given a vector bundle, its (stable) order is the smallest positive integer n such that the n-fold self-Whitney sum is (stably) trivial. So far, the order and the stable order of the canonical vector bun- dle over configuration spaces of Euclidean spaces have been studied by F.R. Cohen, R.L. Cohen, N.J. Kuhn and J.L. Neisendorfer [5], F.R. Cohen, M.E. Mahowald and R.J. Milgram [7], and S.W. Yang [17]. Moreover, the order and the stable order of the canonical vec- tor bundle over configuration spaces of closed orientable Riemann surfaces with genus greater than or equal to one have been studied by F.R. Cohen, R.L. Cohen, B. Mann and R.J. Milgram [6]. In this paper, we mainly study the order and the stable order of the canonical vector bundle over configuration spaces of disjoint unions of spheres.

## Submission history

From: Shiquan Ren [view email]**[v1]**Mon, 16 May 2016 11:54:25 GMT (14kb)

**[v2]**Sat, 20 May 2017 03:05:01 GMT (14kb)

**[v3]**Wed, 21 Mar 2018 02:28:00 GMT (16kb)

**[v4]**Wed, 4 Apr 2018 04:21:39 GMT (16kb)

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