Title: On the cobordism groups of O-manifolds 

Abstract: Given a smooth manifold, a tangential O-structure is a lift of the classifying map of its tangent bundle to BO. An O-manifold is a manifold equipped with an equivalence class of tangential O-structures. The cases n=2 and n=4 recover the familiar notions of oriented and spin manifolds. Larger values of n furnish higher analogs of these with additional geometric properties. In this thesis, we calculate the 2-primary component of the cobordism groups of compact O-manifolds in a range of degrees, for n between 9 and 17. We derive various consequences for the parallelizability of the boundaries of almost-closed manifolds. 

Time: Mar 13, 2026 10:30 AM Eastern Time 

In-person location: 1146 Faculty/Administration Building

Zoom link for online audience: https://wayne-edu.zoom.us/j/98110569399?pwd=HwgOAjduBRelwZS3weV2ybSfEZN3WJ.1

Meeting ID: 981 1056 9399

Passcode: 267958