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Results tagged with at.algebraic-topology
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user 17644
Homotopy theory, homological algebra, algebraic treatments of manifolds.
2
votes
0
answers
578
views
Homotopy equivalence of Lens spaces
I find the following statement about the homotopy equivalence of Lens spaces in Wikipedia. The three-dimensional spaces $L(p,q_1)$ and $L(p,q_2)$ are homotopy equivalent if and only if $q_1 q_2\equiv …
- 2,273
10
votes
2
answers
610
views
Rational homology sphere that is not Seifert manifold
I wonder if there is an example of rational homology sphere that is not a Seifert manifold. If there is, how can one construct such a rational homology sphere from a surgery of a knot in $S^3$?
- 2,273
9
votes
1
answer
323
views
Non-triviality of a Postnikov class in $H^3\left(B \operatorname{PSU}(N) ; \mathbb{Z}_q\right)$
Let $\alpha\in H^2(B\operatorname{PSU}(N) ; \mathbb{Z}_N)$ be the obstruction class for lifting a $\operatorname{PSU}(N)$-bundle to an $\mathrm{SU}(N)$-bundle. Note that $\operatorname{PSU}(N)\cong \o …
- 2,273
12
votes
Mathematical/Physical uses of $SO(8)$ and Spin(8) triality
Seiberg and Witten showed that the $\mathcal{N}=2$ supersymmetric SU(2) gauge theory with $N_f=4$ flavor is endowed with SO(8) flavor symmetry, and it enjoys SO(8) triality.
Later, Gaiotto's construc …
- 2,273