Ping-ponging between relations in groups and relations in quandles
2015 ◽
Vol 24
(07)
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pp. 1550034
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We give elementary proofs of certain relations in the mapping class group of a closed surface of genus 2, MCG (F2, 0). We generalize portions of these to relations in quandles with certain types of elements, associated to a relatively broad class of groups (including mapping class groups), and derive further similar quandle relations. We show these quandle relations correspond to 2-cycles in the homology of racks of tuples of quandle elements, and thence to families of commutation relations back in the groups. The recurrence of some of these phenomena within higher level structures is also explored, as are multiple types of modifications yielding different relations. The constructions are quite malleable in this respect.
2001 ◽
Vol 10
(05)
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pp. 763-767
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2017 ◽
Vol 26
(07)
◽
pp. 1750037
Keyword(s):
1998 ◽
Vol 123
(3)
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pp. 487-499
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