A co-operational bivariant theory derived from cohomology operations

TL;DR

This paper introduces a new co-operational bivariant theory derived from cohomology operations, extending the dual framework of Fulton--MacPherson's theory and relating to Quillen's Steenrod power operations.

Contribution

It defines a generalized cohomology operation for continuous maps with sections and constructs a co-operational bivariant theory based on cohomology operations.

Findings

Defines a generalized cohomology operation related to Steenrod powers

Constructs a co-operational bivariant theory from cohomology operations

Establishes the theory as a subtheory of existing co-operational bivariant theories

Abstract

A co-operational bivariant theory is a ``dual" version of Fulton--MacPherson's operational bivaiant theory. For a given contravariant functor we define a generalized cohomology operation for continuous maps having sections, using cohomology operations. This generalized cohomology operation is related to Quillen's Steenrod power operation. Using this generalized cohomology operation, we define \emph{a co-operational bivariant theory derived from cohomology operations}, which is a subtheory of the co-operational bivariant theory associated to the contravariant functor.