Characteristic numbers and equivariant homotopy type
Abstract
The invariance of characteristic numbers under equivariant homotopy equivalence is studied for odd order group actions. A special set of generators for the rational equivariant bundle bordism modules are constructed. By realizing certain linear combinations of these bundles it is proved that under the gap hypothesis the only homotopy invariant characteristic numbers are rational multiples of the Atiah-Singer G-signature; the equivariant analogue of a well known theorem of P. J. Kahn. If the homotopy equivalence is an isovariant transverse linear one it is shown that the equivariant Euler number is also homotopy invariant.
Degree
Ph.D.
Advisors
Schultz, Purdue University.
Subject Area
Mathematics
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