Topology of Combinatorial Diierential Manifolds

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Combinatorial Differential Topology and Geometry

A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifo...

Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Localizable Invariants of Closed Combinatorial Manifolds and Euler Characteristic

If a real value invariant of closed combinatorial manifolds admits a local formula that depends only on the f -vector of the link of each vertex, then the invariant must be proportional to the Euler characteristic.

Toric Topology and Complex Cobordism

We plan to discuss how the ideas and methodology of Toric Topology can be applied to one of the classical subjects of algebraic topology: finding nice representatives in complex cobordism classes. Toric and quasitoric manifolds are the key players in the emerging field of Toric Topology, and they constitute a sufficiently wide class of stably complex manifolds to additively generate the whole c...