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May
19 |
comment |
Geodesic equation from Christoffel symbols
The answer depends on which is your favourite definition of a geodesic. A possibility would be to take that equation as the definition of a geodesic. |
Apr
20 |
answered | Physical and real life interpretation of the concept of regularity used in differential equations? |
Feb
16 |
comment |
How to compute Conley-Zehnder indices on prequantization spaces?
Can you give a more precise reference, for example to the sections you are referring to? |
Feb
16 |
comment |
What is the character that compactifies $\mathbb{R}$ through the Gelfand transform?
Are you sure that the Stone–Čech compactification of $\mathbb{R}$ is the one-point compactification? This seems to contradict the universal property stated here: en.wikipedia.org/wiki/… For example, not all continuous functions from $\mathbb{R}$ to $[0,1]$ factor through a map from $S^1$. |
Dec
21 |
answered | Trying to Understand Lefschetz Pencils |
Jun
25 |
awarded | Yearling |
Jun
10 |
awarded | Commentator |
Jun
10 |
comment |
Contact structures and adjunction inequality in 3-manifolds
Yes, but this works for Spin^c structures which are extremal for the adjunction inequality. I don't know what happens in general if M is irreducible but the Spin^c structure is not extremal. In lens spaces one can find examples of Spin^c structures which do not come from tight contact structures, but this is a cheat because lens spaces are rational homology spheres and the adjunction inequality for them is empty. Unfortunately my box of examples contains only Seifert manifolds, which do not help much here. |
Jun
10 |
answered | Contact structures and adjunction inequality in 3-manifolds |
Jun
7 |
answered | Research topics restricted to students at top universities? |
Jun
1 |
comment |
Fibration in the 3 torus.
The plural of torus is tori. |
Dec
30 |
comment |
2Pi and 4Pi rotations in the Pin(1,3) group
I don't know if it is the best possible reference, but I've learnt this stuff from the first chapter of Morgan's book "Seiberg-Witten equations and the topology of four-manifolds". |
Dec
29 |
answered | 2Pi and 4Pi rotations in the Pin(1,3) group |
Dec
25 |
answered | Applications of Floer homology |
Dec
23 |
comment |
maslov index of a holomorphic disk
You should look at some standard reference in symplectic topology: I suggest McDuff-Salamon "Holomorphic curves in symplectic topology" or Seidel's book. Then, you can look at Lipshitz's paper "A cylindrical reformulation of Heegaard Floer homology" where he proves the combinatorial formula for the Maslov indexin Heegaard Floer homology. |
Nov
4 |
awarded | Critic |
Oct
10 |
comment |
Exotic Spheres Signature
Your claim sounds bizarre: take your favourite 4n-manifold with non-zero signature and remove a ball: then you have a 4n-manifold with non-zero signature, bounding a homotopy sphere, which is however the standard sphere. |
Oct
7 |
comment |
What is knot contact homology?
You should look at the papers where knot contact homology has been defined: arxiv.org/abs/1109.1542 and its references |
Oct
3 |
comment |
Topology of K3 as a sum of two abelian fibrations.
Try to look at the book of Gompf and Stipsicz |
Oct
1 |
comment |
photon propagator
Unfortunately your first equation goes over the links on the right. |