Cobcat and singular bordism

A. K. Das and S. S. Khare

Vol. 155 (1992), No. 2, 215–227

DOI: 10.2140/pjm.1992.155.215

Abstract

Dold proved that a homomorphism ϕ : Hⁿ(BO) → ℤ₂ corresponds to a manifold Mⁿ if and only if ϕ(Sq^pu + v_p ⋅ u) = 0, ∀p ≥ 0 and ∀u ∈ H^n−p(BO), v_p being the Wu class. The object of the present work is to have a singular analogue of this result and to study the bordism classification of singular manifolds in BO.

Mathematical Subject Classification 2000

Primary: 57R75

Secondary: 55M30

Milestones

Received: 19 February 1991

Revised: 8 July 1991

Published: 1 October 1992