Smooth $S^{1}$ -action and bordism

Mathematische Zeitschrift Bordism of semi-free S1-actions

We calculate geometric and homotopical bordism rings associated to semi-free S1 actions on complex manifolds, giving explicit generators for the geometric theory. The classification of semi-free actions with isolated fixed points up to cobordism complements similar results from symplectic geometry.

Arithmetic and Complex Bordism

Bordism theories are particular sorts of homology theories, built in accordance to the rule singular homology : simplices :: bordism : manifolds. Fixing a structure group G, the geometric chain complex GC∗(X ;G) of a space X is given by GCn(X ;G) =N f : M →X M a connected manifold with G-structure . The boundary maps in this complex are induced by the restriction of f to the boundary of M . Hen...

Complex Bordism*

We give the basic definitions for the complex bordism groups of manifolds and survey some foundational results in the subject.

The Su-bordism Theory

Bordism, and Free Group Actions

In this paper we give characteristic class formulae for all semicharacteristic classes of all compact, closed manifolds with finite fundamental groups. These invariants are identified with elements in certain odd L-groups, and exactly which elements occur is specified. An appendix calculates the cohomology of the model groups needed. A second appendix determines the structure of the L-groups ne...