Timeline for How to calculate Dr. Curt McMullen's expanding eigenvalues for totally degenerate groups?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2011 at 13:17 | vote | accept | steve | ||
| Sep 6, 2011 at 13:02 | vote | accept | steve | ||
| Sep 6, 2011 at 13:03 | |||||
| Sep 5, 2011 at 18:47 | answer | added | Ian Agol | timeline score: 5 | |
| Sep 2, 2011 at 23:01 | comment | added | steve | To clarify my question as best I can, I wish to calculate the expanding eigenvalue of the derivative of the pseudo-Anosov map [2 1; 1 1] at the fixed point (please refer in particular to page 72 of Dr. McMullen's book). Of course, this is the most narrow interpretation of my question. More broadly, I wish to transform my understanding of Dr. McMullen's construction, now fragmentary, to comprehensive, and a few basic points should allow for this transformation. | |
| Sep 2, 2011 at 16:32 | comment | added | steve | Dr. Nead, I believe that you have put the correct words in my mouth. In this case, a few issues have given me pause: 1. How do I work with the monodromy [2 1; 1 1] and the closed singular geodesic? 2. In "Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds", Dr. Brock seems to imply that a totally degenerate group arises as a subgroup resulting from the iteration of a mapping class with both pseudo-Anosov and finite-order restrictions. 3. Dr. Kapovich (pp. 212-213 of his recent book) discusses the existence of McMullen's groups. | |
| Sep 2, 2011 at 14:51 | comment | added | steve | I would like to thank David Roberts, jc, Will Jagy and Sam Nead for their editing and comments. I will answer Will Jagy first. It is probably obvious that I am not a mathematician. Rather, I am a biochemist with a Master's degree, and I am attempting to learn this mathematics in order to apply it to a problem in biochemistry. jc, your point is well-taken, and I believe that Sam Nead addressed your comment concisely. Humility compels me to say that it has taken years of studying mathematics to even ask this question, as badly formulated as it is. | |
| Sep 2, 2011 at 7:31 | comment | added | Sam Nead | Are you asking "What are the eigenvalues of the monodromy of the torus bundle?"? | |
| Sep 2, 2011 at 0:47 | comment | added | Will Jagy | Steve, we really need to know more of your background. What courses have you taken that relate to this? | |
| Sep 2, 2011 at 0:22 | comment | added | David Roberts♦ | I couldn't read such a dense block of text, so I added some white space. This will help people understand what you are trying to ask :) | |
| Sep 2, 2011 at 0:21 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Made massive block of text slightly more readable
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| Sep 1, 2011 at 22:55 | comment | added | j.c. | Could you give some specific details in your post on what you tried and where precisely you got lost (e.g. with a short quotation or summary of the section of the book)? Your question taken literally "What is required in order to derive ..." is quite broad. | |
| Sep 1, 2011 at 20:45 | comment | added | steve | Dr. Rivin, you may be assured that I have, more than once and over a year ago. Dr. McMullen was kind enough to send the input file for drawing the "snowflake" limit set with his lim program. Given the constraints on his time, it is understandable that he could not respond to my inquiries for further information about this "snowflake" group. Turning your question on its head, I consider you to be a top candidate for providing a correct answer. | |
| Sep 1, 2011 at 19:57 | comment | added | Igor Rivin | Since Dr. McMullen is alive, well, and in full possession of his faculties, why not ask him? | |
| Sep 1, 2011 at 16:30 | history | asked | steve | CC BY-SA 3.0 |