Given adjacent subanalytic strata $(X,Y)$ in ${\mathbf{R}}^n$ verifying Kuo’s ratio test $\left(r\right)$ (resp. Verdier’s $\left(w\right)$-regularity) we find an open dense subset of the codimension $k$$C^1$ submanifolds $W$ (wings) containing $Y$ such that $(X\cap W,Y)$ is generically Whitney $\left(b^{\pi }\right)$-regular is exactly one more than the dimension...

A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need to find and...

We prove that Witten’s Conjecture [40] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with $b_1=0$ and odd $b_2^{+}\ge 3$ follows from our $\left(3\right)$-monopole cobordism formula [6] when the four-manifold has $c_1^2\ge {\chi }_h-3$ or is abundant.