Order of the canonical vector bundle over configuration spaces of spheres
-
Shiquan Ren
Abstract
Given a vector bundle, its (stable) order is the smallest positive integer t such that the t-fold self-Whitney sum is (stably) trivial.
So far, the order and the stable order of the canonical vector bundle over configuration spaces of Euclidean spaces have been studied in
[F. R. Cohen, R. L. Cohen, N. J. Kuhn and J. A. Neisendorfer, Bundles over configuration spaces, Pacific J. Math. 104 1983, 1, 47–54],
[F. R. Cohen, M. E. Mahowald and R. J. Milgram, The stable decomposition for the double loop space of a sphere, Algebraic and Geometric Topology (Stanford 1976), Proc. Sympos. Pure Math. 32 Part 2, American Mathematical Society, Providence 1978, 225–228],
and
[S.-W. Yang, Order of the Canonical Vector Bundle on
Acknowledgements
The present author would like to express his deep gratitude to Professor Frederick R. Cohen and Professor Jie Wu for their kind guidance and helpful encouragement on this topic. The present author would like to thank the referee for the valuable comments and helpful suggestions.
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Upper bounds for geodesic periods over rank one locally symmetric spaces
- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
- A realization theorem for sets of lengths in numerical monoids
- On the non-existence of the Mackey topology for locally quasi-convex groups
- The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces
- The cup product of Brooks quasimorphisms
- Heat kernel estimates for time fractional equations
- Extreme non-Arens regularity of the group algebra
- Rational homology and homotopy of high-dimensional string links
- Global integrability for solutions to some anisotropic problem with nonstandard growth
- Hardy operators on Musielak–Orlicz spaces
- Contractibility of the stability manifold for silting-discrete algebras
- Order of the canonical vector bundle over configuration spaces of spheres
- An endpoint version of uniform Sobolev inequalities
- Space-time L2 estimates, regularity and almost global existence for elastic waves
- k-spaces and duals of non-archimedean metrizable locally convex spaces
- Path homology theory of multigraphs and quivers
Artikel in diesem Heft
- Frontmatter
- Upper bounds for geodesic periods over rank one locally symmetric spaces
- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
- A realization theorem for sets of lengths in numerical monoids
- On the non-existence of the Mackey topology for locally quasi-convex groups
- The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces
- The cup product of Brooks quasimorphisms
- Heat kernel estimates for time fractional equations
- Extreme non-Arens regularity of the group algebra
- Rational homology and homotopy of high-dimensional string links
- Global integrability for solutions to some anisotropic problem with nonstandard growth
- Hardy operators on Musielak–Orlicz spaces
- Contractibility of the stability manifold for silting-discrete algebras
- Order of the canonical vector bundle over configuration spaces of spheres
- An endpoint version of uniform Sobolev inequalities
- Space-time L2 estimates, regularity and almost global existence for elastic waves
- k-spaces and duals of non-archimedean metrizable locally convex spaces
- Path homology theory of multigraphs and quivers
