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Tag: simplicial complexes
Home Posts tagged "simplicial complexes"

Tag: simplicial complexes

The dunce hat and Lusternik-Schnirelmann
Graph theory

The dunce hat and Lusternik-Schnirelmann

By oliverknill March 25, 2018 March 26, 2018  dunca hat, homology sphere, interaction cohomology, simplicial complexes

The interaction cohomology of the dunce hat is computed. We then comment on the discrete Lusternik-Schnirelmann theorem.

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The Hydrogen Relation
discrete geometry, Graph theory

The Hydrogen Relation

By oliverknill March 4, 2018 March 7, 2018  graphs, hydrogen, simplicial complexes, spectral radius

For a one-dimensional simplicial complex, the sign less Hodge operator can be written as L-g, where g is the inverse of L. This leads to a Laplace equation shows solutions are given by a two-sided random walk.

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Green Star Formula
discrete geometry, Graph theory

Green Star Formula

By oliverknill January 28, 2018 February 5, 2018  green function, simplicial complex, simplicial complexes

We found a formula of the green function entries g(x,y). Where g is the inverse of the connection matrix of a finite abstract simplicial complex. The formula involves the Euler characteristic of the intersection of the stars of the simplices x and y, hence the name.

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Strong Ring of Simplicial Complexes
Graph theory, quantum calculus

Strong Ring of Simplicial Complexes

By oliverknill July 30, 2017 August 5, 2017  graphs, simplicial complexes, strong ring

The strong ring is a category of geometric objects G which are disjoint unions of products of
simplicial complexes. Each has a Dirac operator D and a connection operator L. Both are related in
various ways to topology.

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