Bordism of oriented \(4\)-manifolds with \(T\)-structure
This paper calculates the cobordism group of oriented 4-manifolds with \(T\) structure (or local action of tori). These are manifolds with local actions of tori which fit together compatibly, and the local actions form a \(T\) structure if they are fixed-point-free. Examples given include bundles with toral fibers, which are not toral actions. The main result is that the cobordism group is \(Z\), determined by the signature. Thus manifolds which are cobordant are cobordant as manifolds with \(T\) structure (or local action of tori).
scientific article; zbMATH DE number 1308043