Vol. 14, No. 1, 2021

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Factorizations of surjective maps of connected quandles

Tori Braun, Charlotte Crotwell, Alfred B.H. Liu, Paul Weston and David N. Yetter

Vol. 14 (2021), No. 1, 53–64

We consider the problem of when one quandle homomorphism will factor through another, restricting our attention to the case where all quandles involved are connected. We provide a complete solution to the problem for surjective quandle homomorphisms using the structure theorem for connected quandles of Ehrman et al. (J. Knot Theory Ramifications 17:4 (2008), 511–520) and the factorization system for surjective quandle homomorphisms of Bunch et al. (J. Knot Theory Ramifications 19:9 (2010), 1145–1156) as our primary tools.

quandles, quandle homomorphisms, factorization
Mathematical Subject Classification 2010
Primary: 20N05
Secondary: 57M25
Received: 24 September 2019
Accepted: 2 November 2020
Published: 4 March 2021

Communicated by Józef H. Przytycki
Tori Braun
Department of Mathematical Sciences
Ripon College
Ripon, WI
United States
Charlotte Crotwell
Department of Mathematics
University of South Carolina
Columbia, SC
United States
Alfred B.H. Liu
Department of Mathematics, Statistics and Computer Science
St. Olaf College
Northfield, MN
United States
Paul Weston
Department of Mathematics and Statistics
Boston University
Boston, MA
United States
David N. Yetter
Department of Mathematics
Kansas State University
Manhattan, KS
United States