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Questions tagged [topology]

In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.

In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.

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What is known about the topological structure of spacetime?

General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions: What topological restrictions do Einstein's equations put on the manifold? For instance, the existence…
Eric
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Intuitively, why are bundles so important in Physics?

I've seem the notion of bundles, fiber bundles, connections on bundles and so on being used in many different places on Physics. Now, in mathematics a bundle is introduced to generalize the topological product: describe spaces that globally are not…
Gold
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Book covering differential geometry and topology for physics

I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory…
user7757
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Why is there no theta-angle (topological term) for the weak interactions?

Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken?
Henry
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Applications of Algebraic Topology to physics

I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most invariants and constructions in algebraic topology…
Sean Tilson
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Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
Nathan BeDell
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Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our physical theories with the assumption of a flat or…
user55867
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Quantum mechanics on a manifold

In quantum mechanics the state of a free particle in three dimensional space is $L^2(\mathbb R^3)$, or more accurately, the projective space of that Hilbert space. Here I am ignoring internal degrees of freedom; otherwise it would be $L^2(\mathbb…
MBN
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Nuclear Fusion: Why is spherical magnetic confinement not used instead of tokamaks in nuclear fusion?

In nuclear fusion, the goal is to create and sustain (usually with magnetic fields) a high-temperature and high-pressure environment enough to output more energy than put in. Tokamaks (donut shape) have been the topology of choice for many years.…
Valentina
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Is there a physical system whose phase space is the torus?

NOTE. This is not a question about mathematics and in particular it's not a question about whether one can endow the torus with a symplectic structure. In an answer to the question What kind of manifold can be the phase space of a Hamiltonian…
joshphysics
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What is the magnetic flux through a trefoil knot?

Imagine a closed loop in the shape of a trefoil knot (https://en.wikipedia.org/wiki/Trefoil_knot). How should one calculate the flux through this loop? Normally we define an arbitrary smooth surface, say, $\mathcal{S}$ whose boundary…
hyportnex
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Can general relativity be completely described as a field in a flat space?

Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?
Anixx
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Why is de Rham cohomology important in fundamental physics?

I'm currently working on some mathematical aspects of higher-spin gravity theories and de Rham cohomology pops up quite often. I understand its meaning as the group of closed forms on some space, modulo the exact forms. Before diving into concrete…
user20250
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Does topology have any role in classical physics?

I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common? Is there any intuitive explanation of why topology is so important? Is…
jinawee
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Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In particular, there should be non-orientable…
user1532
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