Timeline for What is the geometric interpretation of this quantity?
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13 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Jul 30, 2018 at 22:44 | comment | added | Ali Taghavi | I agree with your comment and my +1 for that. But I am just curious in the following question(Sorry, if it is elementary, to be honest , for the moment I have no access to the book of McDuff) Is there a concept of Contact capacity, the biggest disk in $\mathbb{R}^{2n+1}$ with its standard contact structure, which can be contactly embeded in a given contact manifold? | |
| Apr 6, 2014 at 8:23 | vote | accept | Ali Taghavi | ||
| Jan 8, 2014 at 17:34 | comment | added | alvarezpaiva | I don't want to sound mean spirited, but posting questions which should be research level and knowing only the basic definitions may not lead to interesting exchanges. Pick up McDuff and Salamon, it's a great book. | |
| Jan 8, 2014 at 17:25 | comment | added | Ali Taghavi | I know only the basic definitions | |
| Jan 8, 2014 at 17:24 | comment | added | alvarezpaiva | How much do you know of symplectic geometry (from where should I explain)? | |
| Jan 8, 2014 at 17:19 | comment | added | Ali Taghavi | the $\lambda$ in your comment is a constant. But I do not understand the relation to computation of capacity of $D_{r}(M)$. Perhaps I do not underestand a simple fact, I would appreciate if you explain. | |
| Jan 8, 2014 at 17:09 | comment | added | alvarezpaiva | The "classic" text is McDuff, Salamon "Introduction to symplectic topology". | |
| Jan 8, 2014 at 17:07 | comment | added | Ali Taghavi | thank you very much for your comment, could you please introduce me a reference with minimum necessary background? | |
| Jan 8, 2014 at 16:51 | comment | added | alvarezpaiva | $V(r)$ has order $n$: when you dilate in the tangent bundle you only dilate in the direction of the velocities (half the dimension of the total space). Every capacity satisfies $c(M, \lambda \omega) = \lambda c(M, \omega)$ for $\lambda > 0$ (and, yes, this is basically immediate for Gromov width). Since dilation in the velocities dilates the symplectic form, you need to use the exponent $n$ on both the capacity and the volume so that the question be meaningful. | |
| Jan 8, 2014 at 16:38 | comment | added | Ali Taghavi | thank you very much for your interesting answer. I apologize if my question is elementary; is it obvious that the capacity is homogeneous of order 1? assuming this, what is the the true exponent in definition of $C(r)$, $n$ or $2n$, because $V(r)$ is probably of order $n$(and what is reason for this last statement?) | |
| Jan 7, 2014 at 10:47 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
deleted 3 characters in body
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| Jan 7, 2014 at 10:42 | history | answered | alvarezpaiva | CC BY-SA 3.0 |