Self-intersection numbers of curves on the punctured torus
| dc.creator | Chas, Moira | |
| dc.creator | Phillips, Anthony | |
| dc.date | 2009-01-20 | |
| dc.date.accessioned | 2026-07-07T12:32:06Z | |
| dc.date.available | 2026-07-07T12:32:06Z | |
| dc.description | The minimum number of self-intersection points for members of a free homotopy class of curves on the punctured torus is bounded above in terms of the number L of letters required for a minimal description of the class in terms of the generators of the fundamental group and their inverses: it is less than or equal to (L-2)^2/4 if L is even, and (L-1)(L-3)/4 if L is odd. The classes attaining this bound are explicitly described in terms of the generators; there are (L-2)^2 + 4 of them if L is even, and 2(L-1)(L-3) + 8 if L is odd; similar descriptions and totals are given for classes with self-intersection number equal to one less than the maximum. Proofs use both combinatorial calculations and topological operations on representative curves. Computer-generated data are tabulated counting, for each non-negative integer, how many length-L classes have that self-intersection number, for each length L less than or equal to 12. Experimental data are also presented for the pair-of-pants surface. | |
| dc.description | 39 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/0901.2974 | |
| dc.identifier | http://arxiv.org/abs/0901.2974 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216671 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M05, 57N50 | |
| dc.title | Self-intersection numbers of curves on the punctured torus | |
| dc.type | text |