In this paper we construct some invariants of spatial graphs by disk-summing the constituent knots and show the delta edge-homotopy invariance of them. As an application, we show that there exist infinitely many slice spatial embeddings of a planar graph up to delta edge-homotopy, and there exist infinitely many bounda…
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5 results for “edge-homotopy”
The paper classifies clover links using Milnor invariants and edge-homotopy.
problem Classifying clover links using Milnor invariants and edge-homotopy.
method Constructing a bottom tangle from a clover link, defining Milnor numbers for bottom tangles, and proving equivalence based on vanishing Milnor numbers.
result Two clover links are equivalent up to edge-homotopy and -equivalence if their Milnor numbers of length 2k+1 or less are equal.
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples…
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split li…
Investigates Milnor invariants of clover links, defining certain invariants under specific conditions.
problem Investigating indeterminacy in Milnor invariants of links.
method Introduced clover links to study Milnor invariants, showing well-definedness and non-well-definedness conditions.
result Well-defined Milnor numbers for certain lengths of sequences in clover links, with explicit ranges for specific sequences.