Request resources for mathematical foundations of higher-order topological dynamics in networks

Questions
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1

Wolfram Resources for Higher-Order Topological Dynamics

I’m looking for Wolfram resources to study the following topics. Any guidance would be greatly appreciated as I’ve tried Notebook Assistant and OpenAI Wolfram ChatGPTs without success.

Algebraic Topology

  • Simplicial complexes
  • Homology theory
  • Betti numbers
  • Persistent homology

Discrete Exterior Calculus

  • Boundary operators
  • Hodge theory
  • Hodge Laplacians

Dynamical Systems on Higher-Order Networks

  • Synchronization
  • Topological Kuramoto model
  • Topological pattern formation

Quantum-Inspired Mathematical Formalism

  • Topological spinors
  • Topological Dirac operator
  • Triadic interactions
2

Complete functionality for all of these topics may not be available directly in Wolfram Language, but here is a Wolfram Function Repository item for Betti numbers: https://resources.wolframcloud.com/FunctionRepository/resources/BettiNumbers

There is an excellent collection of related links at the bottom of that page, including a link to the main guide page for Geometric Computation that lists several functions that may interest you: Geometric Computation—Wolfram Documentation

Hopefully this helps get you started!

3

Thank you so much!

4

Also PersistantHomology in the Wolfram Function Repository might be relevant.