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

2014; Cambridge University Press; Volume: 14; Issue: 2 Linguagem: Inglês

10.1017/is014005031jkt266

1865-5394

Thomas Hudson,

Nonlinear Waves and Solitons

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.