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SUMMARY:The Nisnevich topology and the Thom isomorphism - Marcus Zibrowius
 \, University of Cambridge
DTSTART:20100128T163000Z
DTEND:20100128T180000Z
UID:TALK22967@talks.cam.ac.uk
CONTACT:Andreas Holmstrom
DESCRIPTION:To begin with\, I will aim to give a memorable definition of t
 he Nisnevich topology\, illustrate it with some examples and highlight som
 e important properties. In the second half of the talk I will sketch a pro
 of of the Thom isomorphism in A^1-homotopy: given a closed smooth subvarie
 ty Z of a smooth variety X\, the quotient X/(X-Z) is homotopy equivalent t
 o the Thom space of the normal bundle of Z in X. In topology this is an ea
 sy consequence of the existence of tubular neighbourhoods. The algebraic p
 roof uses a "deformation to the normal bundle" construction and relies hea
 vily on the use of the Nisnevich topology.
LOCATION:MR11\, Centre for Mathematical Sciences
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