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Results tagged with at.algebraic-topology
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user 6023
Homotopy theory, homological algebra, algebraic treatments of manifolds.
15
votes
Accepted
Examples for non-naturality of universal coefficients theorem
To expand on my comment, let $M = \mathbf{R}P^2$ be the Moore space with (reduced) homology concentrated in dimension $1$. Let $f:M \to \Sigma M$ be the map
$$ M \to S^2 \to \Sigma M $$
given by col …
- 498
28
votes
Counterexamples in algebraic topology?
This is a great question. Here are two of my favorite counterexamples:
Rector proved in 1971 that there are
uncountably many complexes $X$
(distinct in the homotopy category)
such that $\Omega X \s …
4
votes
Dyer-Lashof based spectral sequence for homotopy classes of maps between infinite loop space...
I'm not sure if this is what you want, but Haynes Miller constructs a spectral sequence computing the homology of a connective spectrum $E$ from the homology of $E_0$ as a Hopf algebra over the Dyer-L …
- 498
12
votes
1
answer
633
views
The semidihedral group of order 16 and ko
Let $\mathcal{A}(1)$ denote the subalgebra of the $\mathrm{mod}\ 2$ Steenrod algebra generated by $\mathrm{Sq}^1$ and $\mathrm{Sq}^2$.
The cohomology with $\mathbf{F}_2$ coefficients of the semidihedr …
- 498