We give a formula to detect the oriented bordism class of a codimension one immersion of an oriented 7-manifold in terms of singularities of its singular Seifert surface, that is, a generic map from a compact 8-manifold which extends the given imm...
INDIANA UNIVERSITY MATHEMATICS JOURNAL 61(3) 1111-1127 2012年 [査読有り]
For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the s...
According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket i...
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 43 251-266 2011年4月 [査読有り]
A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self-intersection points equal to-n induces an immersion of the circle bundle over the 2-sphere of Euler class 2n into 4-space. Precomposing these circle bundle imme...
We show that for any given differentiable embedding of the three-sphere in six-space there exists a Seifert surface (in six-space) with arbitrarily prescribed signature. This implies, according to our previous paper, that given such a (6,3)-knot e...
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