Spark complexes on good effective orbifold atlases categorically
Cheng-Yong Du, Lili Shen, Xiaojuan Zhao
TL;DR
This paper develops a categorical framework for spark complexes on effective orbifold atlases, demonstrating their functorial properties and the factorization of the spark character 2-functor.
Contribution
It introduces a 2-functorial construction of spark complexes on good orbifold atlases and shows the compatibility with morphisms between atlases.
Findings
Spark complexes are constructed on good orbifold atlases.
The process is proven to be 2-functorial with compatible systems as morphisms.
The spark character 2-functor factors through this 2-functor.
Abstract
Good atlases are defined for effective orbifolds, and a spark complex is constructed on each good atlas. It is proved that this process is 2-functorial with compatible systems playing as morphisms between good atlases, and that the spark character 2-functor factors through this 2-functor.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology