Bordism of oriented \(4\)-manifolds with \(T\)-structure
type: Item
instance of: scholarly article
title: Bordism of oriented \(4\)-manifolds with \(T\)-structure
zbMATH Open document ID: 0926.57035
DOI: 10.1016/S0166-8641(97)00102-8
author: Piotr Mikrut
published in: Topology and its Applications
publication date: 1999-11-29T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 1308043
zbMATH Keywords: cobordism group
MaRDI profile type: Publication
cites work: Q5589103
cites work: Collapsing Riemannian manifolds while keeping their curvature bounded. I
cites work: Collapsing Riemannian manifolds while keeping their curvature bounded. II
cites work: Smooth G-manifolds as collections of fiber bundles
cites work: Circle Actions on Simply Connected 4-Manifolds
cites work: Cobordism of polarized t-structures
cites work: Smooth \(S^1\)-action and bordism
cites work: On the Structure of Compact Complex Analytic Surfaces, I
cites work: Actions of the Torus on 4-Manifolds. I
cites work: Actions of the torus on 4-manifolds. II
cites work: Action of torus T\(^n\) on (n + 1)-manifolds M\(^{n+1}\)
cites work: The limiting eta invariants of collapsed three-manifolds
cites work: Cobordism groups of semi-free \(S^ 1\)- and \(S^ 3\)-actions
cites work: Geometric 4-manifolds in the sense of Thurston and Seifert 4-manifolds. I
cites work: Q5563920
full work available at URL: s0166-8641(97)00102-8
OpenAlex ID: W2061461016
description: scientific article; zbMATH DE number 1308043