On cobordism of manifolds with corners

Laures, Gerd

doi:10.1090/S0002-9947-00-02676-3

On cobordism of manifolds with corners
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by Gerd Laures

Trans. Amer. Math. Soc. 352 (2000), 5667-5688

DOI: https://doi.org/10.1090/S0002-9947-00-02676-3

Published electronically: August 21, 2000

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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.

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On cobordism of manifolds with corners
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Abstract: