Vol. 294, No. 2, 2018

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ISSN: 0030-8730
Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Jens Hornbostel and Nicolas Perrin

Vol. 294 (2018), No. 2, 401–422
Abstract

We provide several ingredients towards a generalization of the Littlewood–Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott–Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

Keywords
Schubert calculus, cobordism, Grassmannian, generalized cohomology
Mathematical Subject Classification 2010
Primary: 14F43, 14M15, 14N15, 19L41, 55N22
Milestones
Received: 21 March 2017
Revised: 26 September 2017
Accepted: 3 November 2017
Published: 20 February 2018
Authors
Jens Hornbostel
Bergische Universität Wuppertal
Fachgruppe Mathematik und Informatik
Wuppertal
Germany
Nicolas Perrin
Laboratoire de Mathématiques de Versailles, UVSQ, CNRS
Université Paris-Saclay
Versailles
France