Simplicial homology

노트

The term simplicial homology is also used in the literature for the homology of polyhedral spaces, based on the theory of simplicial complexes.^[1]
Simplicial homology arose as a way to study topological spaces whose building blocks are n-simplices, the n-dimensional analogs of triangles.^[2]
Simplicial homology is defined by a simple recipe for any abstract simplicial complex.^[2]
A key concept in defining simplicial homology is the notion of an orientation of a simplex.^[2]
This construction makes simplicial homology a functor from simplicial complexes to abelian groups.^[2]
Abstract : Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information.^[3]
In this article, we use simplicial homology in order to not only compute the topology of a cellular network, but also to discover the clusters of nodes still with no location information.^[3]
The simplicial homology groups and their corresponding Betti numbers are topological invariants that characterize the -dimensional "holes" in the complex.^[4]
The simplicial homology global optimisation (SHGO) algorithm is a general purpose global optimisation algorithm based on applications of simplicial integral homology and combinatorial topology.^[5]