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A coordinate cone in $ℝ^{n}$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $ℝ^{n}$ , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

S-equivalence et congruence de matrices de Seifert: Une conjecture de Trotter.

Eva Bayer (1980)

Inventiones mathematicae

Shellability and the strong gcd-condition.

Berglund, Alexander (2009)

The Electronic Journal of Combinatorics [electronic only]

Shellable Decompositions of Cells and Spheres.

P. Mani, H. Bruggesser (1971)

Mathematica Scandinavica

Simplexwise linear and piecewise linear near self-homeomorphisms of surfaces

Ethan Bloch (1989)

Fundamenta Mathematicae

Simplicial approximation of small multifunctions

Helga Schirmer (1974)

Fundamenta Mathematicae

Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere.

Björner, Anders, Lutz, Frank H. (2000)

Experimental Mathematics

Simplicial maps from the 3-sphere to the 2-sphere.

Madahar, Keerti Vardhan (2002)

Advances in Geometry

Simplicial maps which stabilize to near-homeomorphisms

D. W. Curtis (1972)

Compositio Mathematica

Singularities and exotic spheres

Friedrich Hirzebruch (1966/1968)

Séminaire Bourbaki

Singularities, double points, controlled topology and chain duality.

Ranicki, Andrew (1999)

Documenta Mathematica

SK1 for Finite Group Rings: I.

Robert Oliver (1980)

Inventiones mathematicae

Smooth Equivariant Triangulations of G-Manifolds for G a Finite Group.

Sören Illman (1978)

Mathematische Annalen

Smooth spheres in IR4 with four critical points are standard.

Martin Scharlemann (1985)

Inventiones mathematicae

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 $\leq exp (c (n) d^{α (n) d^{n + 1}})$ . 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 $S^{n - 2} \subset S ⁿ$ , 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.

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