The amazing world of simplicial complexes
arXiv:1804.08211
Abstract
Defined by a single axiom, finite abstract simplicial complexes belong to the simplest constructs of mathematics. We look at a a few theorems.
Notes made for preparing for the AMS special session "Discretization in Geometry" in Boston on April 22, 2018
References in corpus (25)
- On index expectation and curvature for networks
- The McKean-Singer Formula in Graph Theory
- An index formula for simple graphs
- Coloring graphs using topology
- Graphs with Eulerian unit spheres
- Curvature from Graph Colorings
- On Fredholm determinants in topology
- The strong ring of simplicial complexes
- One can hear the Euler characteristic of a simplicial complex
- A cell complex in number theory
- The Jordan-Brouwer theorem for graphs
- Sphere geometry and invariants
- On a Dehn-Sommerville functional for simplicial complexes
- An Elementary Dyadic Riemann Hypothesis
- On the arithmetic of graphs
- Characteristic Length and Clustering
- On Primes, Graphs and Cohomology
- The Cohomology for Wu Characteristics
- Listening to the cohomology of graphs
- On Helmholtz free energy for finite abstract simplicial complexes
- If Archimedes would have known functions
- On Atiyah-Singer and Atiyah-Bott for finite abstract simplicial complexes
- Combinatorial manifolds are Hamiltonian
- Pascal triangle, Stirling numbers and the unique invariance of the Euler characteristic
- The hydrogen identity for Laplacians
Cited by in corpus (11)
- Dehn-Sommerville from Gauss-Bonnet
- Energized simplicial complexes
- Poincare Hopf for vector fields on graphs
- A Reeb sphere theorem in graph theory
- The counting matrix of a simplicial complex
- Integral geometric Hopf conjectures
- The average simplex cardinality of a finite abstract simplicial complex
- Green functions of Energized complexes
- Graph complements of circular graphs
- Division algebra valued energized simplicial complexes
- Complexes, Graphs, Homotopy, Products and Shannon Capacity