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Results tagged with differential-topology
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user 496509
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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An attempt at an alternative calculation of the rank of $\pi_n(MO)$
$\newcommand{\a}{\mathfrak a}\newcommand{\Z}{\mathbb Z}$Let $MO$ be the Thom Spectrum, then I am trying to come up with an alternative calculation that the rank of $\pi_n(MO)$ as a $\Z_2$ vector space …
- 391
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Accepted
An attempt at an alternative calculation of the rank of $\pi_n(MO)$
$\newcommand{\a}{\mathfrak a}\newcommand{\Hom}{\operatorname{Hom}}\newcommand{\Z}{\mathbb Z}$
This can be proven by only assuming that $H^*(MO)$ is a free module. Indeed, due to $H^*(MO)$ being a grad …
- 391
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answer
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What does Robert Stong mean when he says $H^*(MO(k))$ is a free Steenrod algebra in dimensio...
$\newcommand{\Z}{\mathbb Z}\newcommand{\a}{\mathfrak a}\newcommand\widetildeH{\smash{\widetilde H}}$In Robert Stong's notes on Cobordism Theory, on page 95 he asserts the following:
$\widetildeH^* ( …
- 12.9k
3
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1
answer
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Existence (or non existence) of principal bundle charts compatible with an $f$-reduction
I asked this question on math stack exchange here, but I wonder if it would be better received here.
Let $\pi:P\rightarrow M$ and $\pi':P'\rightarrow M$ be principal $G$ and $H$ bundles respectively, …
- 680