2-LC triangulated manifolds are exponentially many

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Maintaining Reeb Graphs of Triangulated 2-Manifolds

Let M be a triangulated, orientable 2-manifold of genus g without boundary, and let h be a height function over M that is linear within each triangle. We present a kinetic data structure (KDS) for maintaining the Reeb graph R of h as the heights of M’s vertices vary continuously with time. Assuming the heights of two vertices of M become equal only O(1) times, the KDS processes O((κ + g)n polyl...

On Stacked Triangulated Manifolds

We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) for a connected closed manifold M of dimension d ≥ 4, if the ith homology group vanishes for 1 < i < d − 1, then any tight triangulation of M is stac...

Triangulated Infinite-dimensional Manifolds

In this paper we extend almost all the results on infinite-dimensional Fréchet manifolds to apply to manifolds modeled on some 2̂ ( = {#£^1 at most finitely many of the coordinates of x are nonzero } ) and we show (Theorem 14) that each /^-manifold has a unique completion to an /2-manifold. (We use h to stand for the Hubert space of all square-summable sequences of some infinite cardinality 31. ...

Many Triangulated 3-Spheres

We construct 2Ω(n 5/4) combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n log n) combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988...