Complexity reduction for path categories
J.F. Jardine
TL;DR
This paper introduces techniques to simplify the computation of path categories in finite simplicial and cubical complexes, including methods for complexity reduction, structure refinement, and parallelization.
Contribution
It presents new methods for reducing complexity and enabling parallel computation of path categories in finite complexes, with focus on cubical structures.
Findings
Complexity reduction techniques for path category calculations.
Refinement methods for cubical complex structures.
A novel approach for parallelizing path category computations.
Abstract
This paper displays complexity reduction techniques for calculations of path categories (or fundamental categories) P(K) for finite simplicial and cubical complexes K. The central technique involves identifying inclusions of complexes for which the induced functor of path categories is fully faithful. Refinements of cubical complex structures are discussed. A first method for parallelizing the calculation of path categories for cubical complexes is introduced.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis