A prismatic classifying space

J. Scott Carter, Victoria Lebed, Seung Yeop Yang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

. 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.

Original languageEnglish
Title of host publicationNonassociative Mathematics and its Applications
EditorsPetr Vojtechovský, Murray R. Bremner, J. Scott Carter, Anthony B. Evans, John Huerta, Michael K. Kinyon, G. Eric Moorhouse, Jonathan D.H. Smith
PublisherAmerican Mathematical Society
Pages43-68
Number of pages26
ISBN (Print)9781470442453
DOIs
StatePublished - 2019
Event4th Mile High Conference on Nonassociative Mathematics, 2017 - Denver, United States
Duration: 29 Jul 20175 Aug 2017

Publication series

NameContemporary Mathematics
Volume721
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

Conference4th Mile High Conference on Nonassociative Mathematics, 2017
Country/TerritoryUnited States
CityDenver
Period29/07/175/08/17

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