On framed bordism.

Framed Bordism and Lagrangian Embeddings of Exotic Spheres

Contents 1. Introduction 1 2. Construction of the bounding manifold 3 3. Transversality 21 4. Preliminaries for gluing 28 5. Construction of an extended gluing map 37 6. Local injectivity of the gluing map 52 7. Gluing near higher codimension strata 61 8. Construction of a smooth manifold with corners 74 9. Triviality of the tangent space of the cobordism 80 Appendix A. Pointwise estimates 88 A...

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...