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Results tagged with at.algebraic-topology
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user 83633
Homotopy theory, homological algebra, algebraic treatments of manifolds.
3
votes
Accepted
Group bundles for topological spaces without universal cover
You are correct that the covering space of the Hawaiian earrings in the picture on p.79 of Hatcher's book cannot be made into a group bundle.
There are other coverings of the Hawaiian earrings which c …
- 666
7
votes
How to compute $[CP^2, G/PL]$?
This is the second half of an answer completing the first half given by @Qiaochu Yuan.
The information we need is that the $k$-invariant is $\beta Sq^2$, and the space $E$ has the $H$-space structure …
- 666
5
votes
Accepted
reference request for mod p and p-adic K-theory
You have learned about topological K-theory (of topological spaces).
The Quillen result from
"On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field", Daniel Quillen, Ann. M …
- 666
8
votes
Is the action of $G$ on $H_1(T^n, \mathbb{Z}) = \mathbb{Z}^n$ faithful?
From Edmonds' notes on Transformation groups:
http://www.indiana.edu/~jfdavis/seminar/transformationgroupsb.pdf
Problem 9. [p.28] Show that if a [finite] group $G$ acts on the torus $T^n$ with a fix …
- 666
14
votes
Accepted
embedding of quaternionic projective spaces
I. M. James, Lectures on algebraic and differential topology, pp. 134–174, Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972,
Theorems 1.2 and 1.3 show that $$N=13.$$
- 666
8
votes
Accepted
induced group actions and covering maps on Eilenberg-Maclane space
If $M$ is connected, then @MarkGrant's fibration sequence gives a long exact sequence on homotopy groups showing that $\pi_1(M/\Sigma_k)\to \Sigma_k$ is surjective. Now apply the $K(-,1)$-functor and …
- 666