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Results tagged with at.algebraic-topology
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user 39521
Homotopy theory, homological algebra, algebraic treatments of manifolds.
19
votes
Accepted
Vietoris-Rips complex homology of a higher degree than the ambient dimension
I have examples for $\ell_2$ distance in $\mathbb{R}^2$.
In particular, take $2n+2$ points at the vertices of a regular polygon of unit radius, and set the distance parameter to be slightly less than …
- 12.4k
11
votes
0
answers
335
views
Lattices and stable homotopy groups of spheres
The number $65520$ arises in two very different scenarios:
It occurs in the formula for the theta series of the Leech lattice:
$$ \Theta_{\Lambda_{24}}(q) = 1 + \sum\limits_{m=1}^{\infty} \dfrac{655 …
- 12.4k
3
votes
Is there a discrete lattice analogue of conformal transformations?
Thurston produced a constructive discretisation of the Riemann mapping theorem which proceeds as follows: given a region $D$, approximate it by densely packing circles into its interior (as a fragment …
- 12.4k