Combinatorial Invariants of Stratifiable Spaces II
Sadok Kallel, Faten Labassi

TL;DR
This paper extends the concept of lego categories to stratifiable spaces, providing new methods for computing their Grothendieck classes and deriving classes of various quotient and configuration spaces.
Contribution
It introduces the notion of lego categories and demonstrates their application in simplifying the computation of Grothendieck classes for complex stratifiable spaces.
Findings
Derived classes of quotient spaces by stratified group actions
Computed classes of crystallographic quotients and polyhedral configuration spaces
Simplified calculations of spaces of 0-cycles
Abstract
In this follow-up to [16], we continue developing the notion of a lego category and its many applications to stratifiable spaces and the computation of their Grothendieck classes. We illustrate the effectiveness of this construction by giving very short derivations of the class of a quotient by the "stratified action" of a discrete group [1], the class of a crystallographic quotient, the class of both a polyhedral product and a polyhedral (or simplicial) configuration space [8], the class of a permutation product [19] and, foremost, the class of spaces of -cycles [11].
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
