Volume 8, issue 1 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On relations and homology of the Dehn quandle

Joel Zablow

Algebraic & Geometric Topology 8 (2008) 19–51
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.

Keywords
quandle homology, Dehn twist, Lefschetz fibration
Mathematical Subject Classification 2000
Primary: 18G60, 57T99
References
Publication
Received: 4 October 2007
Accepted: 22 October 2007
Published: 8 February 2008
Authors
Joel Zablow
Department of Mathematics
Rochester Institute of Technology
85 Lomb Memorial Drive
Rochester NY 14623
USA