K-Witt bordism in characteristic 2

TL;DR

This paper computes the unoriented and oriented bordism groups of K-Witt spaces over fields with characteristic 2, correcting previous errors and discussing remaining ambiguities in certain dimensions.

Contribution

It provides the first complete computation of unoriented bordism groups and a nearly complete computation of oriented bordism groups for K-Witt spaces in characteristic 2, correcting prior errors.

Findings

Complete computation of unoriented bordism groups in characteristic 2

Nearly complete computation of oriented bordism groups with unresolved ambiguities

Correction of previous errors in the author's earlier work

Abstract

This note provides a computation of the bordism groups of K-Witt spaces for fields K with characteristic 2. We provide a complete computation for the unoriented bordism groups. For the oriented bordism groups, a nearly complete computation is provided as well a discussion of the difficulty of resolving a remaining ambiguity in dimensions equivalent to 2 mod 4. This corrects an error in the char(K)=2 case of the author's prior computation of the bordism groups of K-Witt spaces for an arbitrary field K.