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A Thom-Porteous formula for connective K-theory using algebraic cobordism

Published online by Cambridge University Press:  30 June 2014

Thomas Hudson
Thomas Hudson*
Affiliation:
Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, South Korea
*
hudson.t@kaist.ac.kr
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Abstract

Under the assumption that the base field k has characteristic 0, we prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We specialise our formula to connective K-theory providing a geometric interpretation to the double β-polynomials of Fomin and Kirillov by computing the fundamental classes of schubert varieties. As a corollary we obtain a Thom-Porteous formula generalising those of the Chow ring and of the Grothendieck ring of vector bundles.

Keywords

Algebraic cobordismSchubert varietiesFlag bundles
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 2 , October 2014 , pp. 343 - 369
Copyright
Copyright © ISOPP 2014 

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References

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