A Chain Functor For Bordism

The Differentiable Chain Functor Is Not Homotopy Equivalent to the Continuous Chain Functor

Let S∗ and S ∞ ∗ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation i : S∞ ∗ −→ S∗, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

A simplification functor for coalgebras

For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the canonical projections onto the simple factor split, generalizes the well-known notion of simple coalgebras. In case F weakly preserves kernels, the passage from a coalgebra to its simple factor is functorial. This is the simplification functor. It is left adjoint to the inclusion of the subcategor...

Complex Bordism*

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

A Geometric Jacquet Functor

In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homology in geometric terms. The object of this note is to go one step further and describe the Jacquet module functor on Harish-Chandra modules via geometry. Let GR be a real reductive linear algebraic group...

The Su-bordism Theory