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Abstract
We prove that rack (resp. quandle) homology of the free rack (resp. free quandle) is trivial.
ACKNOWLEDGMENT
We would like to thank our colleague Leandro Vendramin for useful comments and conversations. We also thank the referee for comments and corrections of the early version and improvements in the presentation.
Note. The first author remembers and thanks heartily his last visit to Strasbourg, by generous invitation of Jean Louis Loday, and the large list of comments and remarks about rack and quandle homology that he received from him. At that time, in analogy with the relation between groups and Lie algebras, J. L. Loday looked at rack homology as a candidate to replace group homology, if one also replaces Lie algebras with Leibnitz algebras. The question of triviality of the homology of free racks was part of natural conditions for this analogy to work fine. After writing this mauscript, prof. Jean Louis Loday passed away unexpectedly. We dedicate this work to his memory.
Notes
Communicated by J. Alev.