Intersection homology with field coefficients: $K$-Witt spaces and $K$-Witt bordism

TL;DR

This paper constructs examples of pseudomanifolds satisfying Witt conditions for intersection homology with some fields but not others, and extends bordism theory of $K$-Witt spaces to arbitrary fields.

Contribution

It provides geometric examples of $K$-Witt spaces with field-dependent properties and generalizes bordism computations to all fields.

Findings

Examples of pseudomanifolds with field-dependent Witt conditions

Extension of bordism theory of $K$-Witt spaces to arbitrary fields

Insights into intersection homology duality with different coefficient fields

Abstract

We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincare duality with respect to certain fields but not others. We also compute the bordism theory of $K$-Witt spaces for an arbitrary field $K$, extending results of Siegel for $K=Q$.