Questions tagged [geometric-topology]
5 questions
18
votes
5 answers
Applications of Geometric Topology to Theoretical Physics
Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold theory, surgery theory, and other topics are developed…
Samuel Reid
- 444
5
votes
0 answers
What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?
I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry.
One alternative way of formulating it: I am looking for an equivalent of Weaire–Phelan structure that would be able to fill in a…
Andrei Kucharavy
- 151
- 3
2
votes
4 answers
How should observers determine whether they can be described as being "defined on a Lorentzian manifold"?
Consider infinitely many distinguishable observers, no two of whom ever meet; and who generally "keep sight of each other", but not necessarily "each keeping sight of all others".
How should they determine whether or not they can be described as…
user12262
- 4,360
2
votes
0 answers
Physical interpretation of a certain Hamiltonian
Consider a $2 \times 2$ Hermitian (or symmetric) matrix-valued function
$$g(x) = \{ g_{jk}(x)\}_{j,k=1,2}, \quad x \in \mathbb{R}^{2},$$
such that $0 < m_{-}I \leq g(x) \leq m_{+}I$, for some $m_{-}, m_{+} > 0$, where $\mathbb{C}^{2}$ is endowed…
Geno Whirl
- 203
- 1
- 4
-1
votes
2 answers
What's a "noninertial frame"?
In some PSE questions or answers such as here (and comments below) there appears the notion of "accelerating frame" or (more or less equivalently) "noninertial frame".
What's the definition of this notion?,
i.e.
How are given participants (or, if…
user12262
- 4,360