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Journal Articles Contemporary mathematics Year : 2018

A prismatic classifying space


A qualgebra G is a set having two binary operations that satisfy compatibility conditions which are modeled upon a group under conjugation and multiplication. We develop a homology theory for qualgebras and describe a classifying space for it. This space is constructed from G-colored prisms (products of simplices) and simultaneously generalizes (and includes) simplicial classifying spaces for groups and cubical classifying spaces for quandles. Degenerate cells of several types are added to the regular prismatic cells; by duality, these correspond to "non-rigid" Reidemeister moves and their higher dimensional analogues. Coupled with G-coloring techniques, our homology theory yields invariants of knotted trivalent graphs in R3 and knotted foams in R4. We re-interpret these invariants as homotopy classes of maps from S2 or S3 to the classifying space of G.

Dates and versions

hal-02143289 , version 1 (29-05-2019)



Scott J. Carter, Victoria Lebed, Seung Yeop Yang. A prismatic classifying space. Contemporary mathematics, 2018. ⟨hal-02143289⟩
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