Intrinsic Properties of Spatial Graphs - Denison University

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$Math 232 syllabus - Denison University$

$Math 102 syllabus - Personal Pages - Denison University$

Introduction Linking and Knotting Other Intrinsic Properties ConclusionLinking and Knotting in other ManifoldsDefinition (Flapan, Howards, Lawrence, M, 2006)An embedding of a graph G in a 3-manifold M is unknotted ifevery cycle in G bounds a disk in M, and it is unlinked if everypair of disjoint cycles in G bound disjoint disks in M.Theorem (Flapan, Howards, Lawrence, M, 2006)For any 3-manifold M, a graph G is intrinsically linked (resp.knotted) in M if and only if it is intrinsically linked (resp. knotted)in S 3 .Blake MellorIntrinsic Properties of Spatial Graphs
Introduction Linking and Knotting Other Intrinsic Properties ConclusionLinking in RP 3Definition (Foisy et. al.*, 2008)An embedding of a graph G in a 3-manifold M is unlinked if forevery pair of disjoint cycles L 1 and L 2 , both cycles are unknotsand there is a 3-ball A such that L 1 ⊂ A and L 2 ⊂ A c .In particular, in RP 3 , there are two types of unknot: one ishomologically trivial, and the other is not.Blake MellorIntrinsic Properties of Spatial Graphs
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Intrinsic Properties of Spatial Graphs - Denison University

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