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The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

A linear functional on a smooth differential form.

Distinguish between smooth manifolds in four dimensions.

A common mechanism which generates singularities from smooth initial conditions.

A triangle formed by the arcs of three geodesics on a smooth surface.

A smooth manifold with a Poisson bracket defined on its function space.

Given a smooth function f:R^n->R^n, if the Jacobian is invertible at 0, then there is a neighborhood U containing 0 such that f:U->f(U) is a diffeomorphism. That is, there is ...

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

An area-minimizing surface (rectifiable current) bounded by a smooth curve in R^3 is a smooth submanifold with boundary.

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.