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Results tagged with gt.geometric-topology
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user 39521
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
6
votes
Accepted
Space of halfspaces
The space is just $\mathbb{R} \times S^{n-1}$: each oriented hyperplane $H$ is identified by the normal unit vector $v$ together with the inner product of $v$ with an arbitrary $w \in H$.
- 12.4k
23
votes
What is the geometric shape of the Monster sporadic group?
In the penultimate chapter of Sphere Packings, Lattices and Groups, the authors define a $196884$-dimensional real vector space and a faithful representation of the Monster group on that space.
Now, …
- 12.4k
10
votes
There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?
There are no such graphs when $n$ is odd, by the handshaking lemma.
Conversely, for all even $n \geq 224$, we claim such a graph exists.
In particular, given two planar 5-regular graphs $G$, $H$ each …
- 12.4k
4
votes
Unusual symmetries of the Cayley-Menger determinant for the volume of tetrahedra
The following comment in the question intrigued me:
In fact, it's possible to show that the linear symmetries of
$\mathbb{R}^6$ that preserve the Cayley-Menger determinant form the
Weyl group $D_6$, …
- 12.4k