We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an involution, and relations arise from equivariant K-theory characteristic numbers. We investigate in detail the structure of this ring. Concrete applications are provided concerning involutions of varieties, relating the geometry of the ambient variety to that of the fixed locus, in terms of Chern numbers. In particular, we prove an algebraic analog of Boardman’s five halves theorem in topology, of which we provide several generalizations and variations.

Haution, O. (2023). On the algebraic cobordism ring of involutions. ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE, 56(4), 981-1028 [10.24033/asens.2548].

On the algebraic cobordism ring of involutions

Haution, O
2023

Abstract

We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an involution, and relations arise from equivariant K-theory characteristic numbers. We investigate in detail the structure of this ring. Concrete applications are provided concerning involutions of varieties, relating the geometry of the ambient variety to that of the fixed locus, in terms of Chern numbers. In particular, we prove an algebraic analog of Boardman’s five halves theorem in topology, of which we provide several generalizations and variations.
Articolo in rivista - Articolo scientifico
involutions, fixed points, Chern numbers, algebraic cobordism, equivariant cohomology theories
Involutions, points fixes, nombres de Chern, cobordisme algébrique, théories cohomologiques équivariantes
English
2023
56
4
981
1028
open
Haution, O. (2023). On the algebraic cobordism ring of involutions. ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE, 56(4), 981-1028 [10.24033/asens.2548].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/449338
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