Topology Atlas | Conferences

Knots in Washington XXXIII; Categorification of Knots, Algebras, and Quandles; Quantum Computing
December 2-4, 2011
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU),Mark Kidwell (U.S. Naval Academy and GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Mayer-Vietoris sequence for multispindles
by
Krzysztof Putyra
Columbia University
Coauthors: Jozef H. Przytycki

Homology theory for multispindles is motivated by rack homology. It is defined for any set X with a finite number of mutually and self distributive operations *1, ..., *n. Such a set is called a multishelf and, if each *i is idempotent, a multispindle.

Recently, Jozef H. Przytycki and the author have computed the homology for any finite distributive lattice, by reducing every lattice to a Boolean algebra with two elements B2. This method appeared to work for any 2-spindle (X, *1, *2) with absorption:


(x*1 y)*2 y = y = (x*2 y)*1 y

In a general case, there is a long exact sequence of homology, similar to Mayer-Vietoris sequence known in Algebraic Topology. I will explain how this sequence arises for sets with distributive operations. As a result we will see that homology for spindles are almost determined by homology of quandles.

Date received: November 14, 2011

Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbdt-20.