Poincar\'e-Verdier duality in o-minimal structures

TL;DR

This paper establishes a Poincaré-Verdier duality theorem for o-minimal sheaf cohomology, extending classical duality concepts to the setting of o-minimal structures and definable spaces.

Contribution

It proves a duality theorem for o-minimal sheaf cohomology with definably compact supports in definably normal, locally compact spaces within any o-minimal structure.

Findings

Proves Poincaré-Verdier duality in o-minimal sheaf cohomology.

Extends duality concepts to o-minimal structures.

Applicable to definably normal, locally compact spaces.

Abstract

Here we prove a Poincar\'e-Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.