Timeline for How many components are there in the space of "generic" planar N-gons? (Mnev's revenge)
Current License: CC BY-SA 3.0
8 events
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| Jul 18, 2017 at 7:57 | comment | added | Alexandre Eremenko | MR1350697 M. Kapovich, and J. Millson, On the moduli space of polygons in the Euclidean plane. J. Differential Geom. 42 (1995), no. 1, 133–164. | |
| Jul 18, 2017 at 5:01 | comment | added | Richard Montgomery | Maybe the question is easier if the N ordered generic points lie in the real projective plane instead of the affine plane? Then for N=4 we get only 1 component... | |
| Jul 18, 2017 at 3:22 | comment | added | Richard Montgomery |
Thank you j.c. for the references!. The tables here at least seem to yield lower bounds. Perusing the `Handbooks'' I found a table on p. 147 of a chapter titled PSEUDOLINE ARRANGEMENTS'' by Stefan Felsner and Jacob E. Goodman which apparently asserts a lower bound for the number of combinatorial types of the form $2^{4N log N}$ but these are not simple''. I am not sure though if they are talking about the same thing that I am.
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| Jul 18, 2017 at 0:27 | comment | added | j.c. | Nevermind, since your point sets are ordered, the enumeration will be different. There's also potentially the issue mentioned in this question, where mathoverflow.net/questions/98283 , though the answer doesn't seem to give a definitive answer for point configurations in general position. | |
| S Jul 18, 2017 at 0:08 | history | suggested | David G. Stork | CC BY-SA 3.0 |
Fixed quotation marks, used standard definition of "general position," clarified grammar
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| Jul 18, 2017 at 0:06 | comment | added | j.c. | I think what you're after is related to the number of "order types" ist.tugraz.at/aichholzer/research/rp/triangulations/ordertypes | |
| Jul 18, 2017 at 0:01 | review | Suggested edits | |||
| S Jul 18, 2017 at 0:08 | |||||
| Jul 17, 2017 at 23:51 | history | asked | Richard Montgomery | CC BY-SA 3.0 |