# nLab B-bordism

### Context

#### Manifolds and cobordisms

manifolds and cobordisms

# Contemts

## Idea

A $B$-bordism is a cobordism $W$ equipped with extra “topological structure” in the form of a lift of the classifying map $W \to B O$ of its tangent bundle through some fibration $B \to B O$ over the classifying space of the orthogonal group.

Commonly considered are lifts through the Whitehead tower of the orthogonal group), corresponding, in this order, to cobordisms with

etc.

## References

Revised on April 4, 2013 19:05:12 by Diarmuid Crowley? (195.37.209.182)