Symplectic and odd orthogonal Pfaffian formulas for algebraic cobordism

Thomas Hudson and Tomoo Matsumura

Vol. 302 (2019), No. 1, 97–118

DOI: 10.2140/pjm.2019.302.97

Abstract

In the Chow ring of symplectic/odd orthogonal Grassmann bundles the degeneracy loci classes can be expressed as a sum of Schur–Pfaffians. An analogous Schur–Pfaffian formula was obtained for $K$-theory by the authors together with T. Ikeda and M. Naruse. Here we generalize this explicit formula of degeneracy loci classes to algebraic cobordism, which is universal among all oriented cohomology theories.

Keywords

generalised Schubert calculus, algebraic cobordism, pfaffian, isotropic grassmannian

Mathematical Subject Classification 2010

Primary: 14M15, 55N22

Secondary: 05E05, 14C17

Milestones

Received: 16 February 2018

Revised: 25 January 2019

Accepted: 11 February 2019

Published: 5 November 2019