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Results tagged with cobordism
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user 43054
Cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold.
7
votes
Are there non trivial maps from $H\mathbb{Z}$ to $MGL$?
NO such a map does not exist.
Thanks to Eric Peterson for making me realize that the argument carries through even if the map is not a map of algebras.
By rigidity,you can only consider the case whe …
- 16.5k
3
votes
Accepted
Basic question on the cobordism spectrum
A simple way of seeing it is to explicitly spell out what we mean when we say that a spectrum is "presented" by a prespectrum. To say that that a spectrum $E$ is presented by
$$(E_0,E_1,...)$$
means t …
- 16.5k
11
votes
Accepted
Reference on complex cobordism
This is worked out in part 2 of
Adams, J. F., Stable homotopy and generalised homology, Chicago Lectures in Mathematics. Chicago - London: The University of Chicago Press. X, 373 p. £ 3.00 (1974). …
- 16.5k
3
votes
Accepted
(Algebraic) cobordism and the rank function
Let me first write what happens for classical cobordism. You are basically asking whether the map $\operatorname{MU}\to H\mathbb{Z}$ factors through the projection $\operatorname{ku}\to H\mathbb{Z}$. …
- 16.5k
11
votes
Künneth formulas/theorem for bordism groups and cobordisms?
For a general well-behaved homology theory[1] (this includes both ordinary cohomology, K-theory and cobordism) there is a Künneth spectral sequence
$$E^2_{p,q}=\mathrm{Tor}_{p,q}^{E_*}(E_*X,E_*Y)\Rightarrow …
- 16.5k