JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 19(7) 917-933 2010年7月 [査読有り]
A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the...
HOMOLOGY HOMOTOPY AND APPLICATIONS 12(1) 45-60 2010年 [査読有り]
We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular homotopy by the Wu invariant. This result is a generalization of the f...
REVISTA MATEMATICA COMPLUTENSE 23(1) 1-17 2010年1月 [査読有り]
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 th...
TOPOLOGY AND ITS APPLICATIONS 156(17) 2782-2794 2009年11月 [査読有り]
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum...
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 361(4) 1885-1902 2009年 [査読有り]
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 invaria...