Vol. 302, No. 1, 2019

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Symplectic and odd orthogonal Pfaffian formulas for algebraic cobordism

Thomas Hudson and Tomoo Matsumura

Vol. 302 (2019), No. 1, 97–118
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.

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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
Authors
Thomas Hudson
Fachgruppe Mathematik und Informatik
Bergische Universität Wuppertal
Gaußstrasse 20
42119 Wuppertal
Germany
Tomoo Matsumura
Department of Applied Mathematics
Okayama University of Science
Okayama 700-0005
Japan