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- W2951805300 abstract "Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the classical case. Unlike previous attempts at generalizing link homotopy to spatial graphs, our new relation allows analogues of some standard link homotopy results and invariants. In particular we can define a type of Milnor group for a spatial graph under component homotopy, and this group determines whether or not the spatial graph is splittable. More surprisingly, we will also show that whether the spatial graph is splittable up to component homotopy depends only on the link homotopy class of the links contained within it. Numerical invariants of the relation will also be produced." @default.
- W2951805300 created "2019-06-27" @default.
- W2951805300 creator A5077657883 @default.
- W2951805300 date "2007-04-25" @default.
- W2951805300 modified "2023-09-27" @default.
- W2951805300 title "Milnor Invariants for Spatial Graphs" @default.
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