On cobordism of manifolds with corners. (English) Zbl 0954.55008
From author’s abstract: This work sets up a cobordism theory for manifolds with corners and gives an identification with the homotopy of a certain limit of Thom spectra. It thereby creates a geometrical interpretation of Adams-Novikov resolutions and lays the foundation for investigating the chromatic status of the elements so realized. As an application, Lie groups together with their left invariant framings are calculated by regarding them as corners of manifolds with interesting Chern numbers. The work also shows how elliptic cohomology can provide useful invariants for manifolds of codimension 2.
Reviewer: Taras E.Panov (Moskva)
MSC:
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
| 57R20 | Characteristic classes and numbers in differential topology |
| 55Q10 | Stable homotopy groups |
| 55N34 | Elliptic cohomology |
| 55T15 | Adams spectral sequences |
| 57R90 | Other types of cobordism |
Keywords:
cobordism theory; manifolds with corners; Lie groups; Adams-Novikov spectral sequence; elliptic cohomology; Adams-Novikov resolutionsReferences:
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