20.500.12556/RUL-109537 New techniques for computing geometric index We introduce new general techniques for computing the geometric index of a link ▫$L$▫ in the interior of a solid torus ▫$T$▫. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples and allow a simple computation of geometric index for new examples where the index was not previously known. The geometric index measures the minimum number of times any meridional disc of ▫$T$▫ must intersect ▫$L$▫. It is related to the algebraic index in the sense that adding up signed intersections of an interior simple closed curve ▫$C$▫ in ▫$T$▫ with a meridional disc gives ▫$\pm$▫ the algebraic index of ▫$C$▫ in ▫$T$▫. One key idea is introducing the notion of geometric index for solid chambers of the form ▫$B^2 \times I$▫ in ▫$T$▫. We prove that if a solid torus can be divided into solid chambers by meridional discs in a specific (and often easy to obtain) way, then the geometric index can be easily computed. algebraic index geometric index Whitehead link Bing link McMillan link Gabai link Antoine link true false true Angleški jezik Ni določen Članek v reviji 2019-09-05 10:48:23 2019-09-05 10:48:25 2022-08-21 03:42:47 0000-00-00 00:00:00 2017 0 0 Str. 1-15 iss. 6 art. 237 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.124 1660-5446 10.1007/s00009-017-1036-1 18167129 13561433 RAZ_Andrist_Kathryn_B._i2017.pdf RAZ_Andrist_Kathryn_B._i2017.pdf 1 5A2056D5068EB1D1D7091DA3E8034988 9c3258b72973555e8e070cfd0a6f4b1dc0cfe4ee2195941b5665da165154b644 e3c8ad3d-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121112 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0