$3$-dimensional bordism.

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

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...

Hodge Filtered Complex Bordism

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show that the theory satisfies a projective bundle formula and A1-homotopy invarianc...

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...