Questions tagged [dg.differential-geometry]
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
6 questions from the last 7 days
5
votes
1
answer
282
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An intriguingly simple integral functional for star-shaped, planar, simple, closed, smooth curves
The following is a question that popped up in my research in geometric analysis some time ago and that I dropped and kept coming back to multiple times. I will first state the problem, or rather my ...
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4
votes
1
answer
183
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What is the volume of $\Sigma(2, 3, 13)$ associated with its $\widetilde{\operatorname{SL}(2, \mathbb{R})}$ geometry?
I've been considering a research topic based on extending the material from Khoi's research paper concerning a Chern–Simons-type invariant for 3-manifolds, and I'm stuck on a specific problem ...
4
votes
1
answer
201
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Nonautonomous Lie derivative
Let $M$ be a smooth manifold with local coordinates $x = (x^1, \dots, x^m)$, and let $\tilde{M} = (t_1, t_2) \times M$.
Let a vector field $v(t, x) = (v^1, \dots, v^m)$ on $M$ depend on $t$ as a ...
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10
votes
1
answer
325
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Orientation local system of a vector bundle
Let $p:E\to X$ be a rank $k$ real vector bundle on a paracompact space. This question is about possible definitions of the orientation local system of $E$, which should be a local system of integer ...
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1
vote
0
answers
65
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Heat kernel ratio on flat torus T² for specific winding sectors
Consider the heat kernel (Euclidean propagator) for a free particle on the space $T² × R³$, where $T²$ is a flat torus with radii $R₁$ and $R₂$.
The return amplitude for a path constrained to winding ...
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6
votes
2
answers
555
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When is a symplectic manifold with the opposite orientation itself symplectic?
Suppose $(M,\omega)$ is a closed (compact without boundary) symplectic manifold of dimension $2n$. Suppose $\overline{M}$ is a homeomorphic copy of $M$ with the opposite (reverse) orientation. My ...
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