Algebraic vector bundles on spheres
By A. Asok, Jean Fasel. 2012
77 citations recorded by the source corpus.
We determine the first non‐stable A1 ‐homotopy sheaf of SL n . Using techniques of obstruction theory involving the A1 ‐Postnikov tower, supported by some ideas from the theory of unimodular rows, we classify vector bundles of rank at least d‐1 on split smooth affine quadrics of dimension 2d‐1 . These computations allow us to answer a question posed by Nori, which gives a criterion for completability of certain unimodular rows. Furthermore, we study compatibility of our computations of A1 ‐homotopy sheaves with real and complex realization.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c4b308946695be2d4223194ae6a2156c795681f4
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In Geometry and Topology
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- M. Levine
- Denis-Charles Cisinski
- Frédéric Déglise
- John E. Harper
- C. Berger
In Mathematical Physics
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- M. Levine
- Denis-Charles Cisinski
- Frédéric Déglise
- John E. Harper
- C. Berger
Citations in the corpus
- The first stable homotopy groups of motivic spheres (2016, background): “es on smooth schemes of finite type, see Morel [39, Theorem 6.2.7], [41, Theorem 2.11]. It is interesting to compare with the computations ofunstable motivic homotopy groupsof punctured affine spaces in [3], [4], [5]. If d > 3, the extension for the unstable homotopy sheaf πd(Ad r{0}) conjectured by”
- Affine representability results in 1–homotopy theory, II : Principal bundles and homogeneous spaces (2015, unknown): “Remark 3 It has been known for some time that an analog of Morel’s theorem should hold for torsors under groups like SL n and Sp 2n (for SL n this is mentioned eg in Asok and Fasel [5, Theorem 4.2]).”