nLab
MP

Contents

Context

Cobordism theory

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

The 2-periodic version of complex cobordism cohomology theory MU is usually denoted MPMP (e.g. Lurie lecture 18, example 5).

Properties

As a Thom spectrum

MPMP may be realized as the Thom spectrum of the universal virtual complex bundle of arbitrary rank over the space BU×B U \times \mathbb{Z} (Lurie lecture 18, Example 5).

Landweber exact functor therem

There is an analogue of the Landweber exact functor theorem for even 2-periodic cohomology theories, with MU replaced by MP (Lurie lecture 18, prop. 11).

flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:

bordism theory\;M(B,f) (B-bordism):

relative bordism theories:

equivariant bordism theory:

global equivariant bordism theory:

algebraic:

References

Last revised on September 23, 2021 at 07:22:05. See the history of this page for a list of all contributions to it.