20.500.12556/RUL-111223 The geometry and fundamental groups of solenoid complements A solenoid is an inverse limit of circles. When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse limits) have different fundamental groups. Embeddings of the same solenoid can give different groups; in particular, the nicest embeddings are unknotted at each level, and give an Abelian fundamental group, while other embeddings have non-Abelian groups. We show using geometry that every solenoid has uncountably many embeddings with nonhomeomorphic complements. solenoid 3-manifold inverse limit embedding fundamental group knot complement braid Jaco-Shalen-Johannson decomposition Mostow-Prasad rigidity true false true Angleški jezik Ni določen Članek v reviji 2019-09-26 07:47:10 2019-09-26 07:47:11 2022-08-23 03:41:38 0000-00-00 00:00:00 2015 0 0 20 str. iss. 14 Vol. 24 2015 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.162 0218-2165 10.1142/S0218216515500698 17540697 3996249 RAZ_Conner_Gregory_R._i2015.pdf RAZ_Conner_Gregory_R._i2015.pdf 1 E1A5C9FE4D1AD799748CF87668C2EF94 5a435829a332f9e098912f8fe2e9c0e845955634d95e81abe37eaeb278d86070 55b8cbd1-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=123050 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0