Intersection-number operators and Chebyshev polynomials. IV: Non-planar cases. (English) Zbl 1186.57013
Summary: We define operators on a ring that allow one to determine the geometric intersection number of two simple closed curves on an oriented surface of genus \(g\geq 0\) with free fundamental group. A variation of these same operators was used in a previous paper to do a similar thing on a punctured disc [AMS/IP Stud. Adv. Math. 24, 49–75 (2001; Zbl 1030.11066)]. This result is used to give a necessary condition for two words in a free group to have the same character under all representations of the free group into \(\mathrm{SL}(2,\mathbb C)\).
MSC:
| 57M50 | General geometric structures on low-dimensional manifolds |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 11T06 | Polynomials over finite fields |
Citations:
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