# MOS

## Seminar

### Vector bundles on the algebraic 5-sphere and punctured affine 3-space

Seminar Room 1, Newton Institute

#### Abstract

The 5-dimensional complex sphere X is isomorphic to SL_3/S_2, which admits a fibration p: X-->Y to the 3-dimensional punctured affine space Y=C^{3}\{0} with C^{2} fibres. It was shown by Fabien Morel that vector bundles on a smooth affine variety are determined by A^{1}-homotopy classes of maps to BGL. The fibration p is an A^{1}-homotopy weak equivalence but the Y above is not affine, so it is natural to look for non-isomorphic vector bundles on Y with isomorphic pull-backs to X. We give interesting examples of such bundles of any rank bigger than 1. The examples are produced from vector bundles on the projective space P=P^2.#### Video

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