The Characteristic Numbers Of The Form [M] Of Vector Bundles And (Z2) K-actions With Fixed Point Set Of Constant Codimension

This doctor graduation dissertation consists of two part. In the first part, we mainly discuss the characteristic numbers of the form [M] of vector bundles, including1. A simple proof of Kosniowski-Stong's formula is given using the fundamental theorem of the bordism theory of manifolds with involutions.2. Define the map , which is closely connected with the characteristic numbers of the form [M], and prove that it's a monomorphism.3. Find special bases of MO and .M whose image under is the simplest.4. A group of generators of Imga expressed by a base of MO is given.In part two, we discuss the (Z2)k-actions with fixed point set of constant codimension and determine the ideal J.