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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On cobordism of manifolds with corners


Author: Gerd Laures
Journal: Trans. Amer. Math. Soc. 352 (2000), 5667-5688
MSC (2000): Primary 55N22, 55T15; Secondary 55Q10, 55N34, 57R20
Published electronically: August 21, 2000
MathSciNet review: 1781277
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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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Additional Information

Gerd Laures
Affiliation: Fachbereich Mathematik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
Address at time of publication: Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: gerd@laures.de

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02676-3
PII: S 0002-9947(00)02676-3
Keywords: Cobordism theory, manifolds with corners, Lie groups, Adams-Novikov spectral sequence, elliptic cohomology
Received by editor(s): June 24, 1998
Published electronically: August 21, 2000
Article copyright: © Copyright 2000 American Mathematical Society