K-Witt bordism in characteristic 2

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.

Corrigendum: Intersection homology with field coefficients: K‐Witt spaces and K‐Witt Bordism

“…In this corrigendum, we state, as far as possible, the correct results. Details can be found in [1].If we consider K-Witt spaces and K-Witt bordism using K-orientations, then for char(K) = 2, this is unoriented bordism, which we denote N K−Witt * .…”

“…In this corrigendum, we state, as far as possible, the correct results. Details can be found in [1].…”

“…See [1] for a discussion of the difficulty in determining which case of item (4) of Theorem 2 holds.…”

“…The argument that Ω K−Witt 4k+2 = 0 given in [2] does not hold when k = 0. However, in this dimension it is not difficult to prove the result directly; details are provided in [1].…”