Displaying 381 – 400 of 507

Showing per page

Smoothing of real algebraic hypersurfaces by rigid isotopies

Alexander Nabutovsky (1991)

Annales de l'institut Fourier

Define for a smooth compact hypersurface M n of R n + 1 its crumpleness κ ( M n ) as the ratio diam R n + 1 ( M n ) / r ( M n ) , where r ( M n ) is the distance from M n to its central set. (In other words, r ( M n ) is the maximal radius of an open non-selfintersecting tube around M n in R n + 1 . ) We prove that any n -dimensional non-singular compact algebraic hypersurface of degree d is rigidly isotopic to an algebraic hypersurface of degree d and of crumpleness exp ( c ( n ) d α ( n ) d n + 1 ) . Here c ( n ) , α ( n ) depend only on n , and rigid isotopy means an isotopy passing only through hypersurfaces of degree...

Some non-trivial PL knots whose complements are homotopy circles

Greg Friedman (2007)

Fundamenta Mathematicae

We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities S n - 2 S , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.

Currently displaying 381 – 400 of 507