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2008 On relations and homology of the Dehn quandle
Joel Zablow
Algebr. Geom. Topol. 8(1): 19-51 (2008). DOI: 10.2140/agt.2008.8.19

Abstract

Isotopy classes of circles on an orientable surface F of genus g form a quandle Q under the operation of Dehn twisting about such circles. We derive certain fundamental relations in the Dehn quandle and then consider a homology theory based on this quandle. We show how certain types of relations in the quandle translate into cycles and homology representatives in this homology theory, and characterize a large family of 2–cycles representing homology elements. Finally we draw connections to Lefschetz fibrations, showing isomorphism classes of such fibrations over a disk correspond to quandle homology classes in dimension 2, and discuss some further structures on the homology.

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Joel Zablow. "On relations and homology of the Dehn quandle." Algebr. Geom. Topol. 8 (1) 19 - 51, 2008. https://doi.org/10.2140/agt.2008.8.19

Information

Received: 4 October 2007; Accepted: 22 October 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.57031
MathSciNet: MR2377276
Digital Object Identifier: 10.2140/agt.2008.8.19

Subjects:
Primary: 18G60, 57T99

Rights: Copyright © 2008 Mathematical Sciences Publishers

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