Quandle coloring and cocycle invariants of composite knots and abelian extensions
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02182165_v25_n5_p_Clark |
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todo:paper_02182165_v25_n5_p_Clark2023-10-03T15:10:51Z Quandle coloring and cocycle invariants of composite knots and abelian extensions Clark, W.E. Saito, M. Vendramin, L. abelian extensions cocycle invariants colorings composite knots Quandle Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of small connected quandles, called Rig quandles. Computer calculations are presented, and summaries of outputs are discussed. © 2016 World Scientific Publishing Company. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02182165_v25_n5_p_Clark |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
abelian extensions cocycle invariants colorings composite knots Quandle |
| spellingShingle |
abelian extensions cocycle invariants colorings composite knots Quandle Clark, W.E. Saito, M. Vendramin, L. Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| topic_facet |
abelian extensions cocycle invariants colorings composite knots Quandle |
| description |
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of small connected quandles, called Rig quandles. Computer calculations are presented, and summaries of outputs are discussed. © 2016 World Scientific Publishing Company. |
| format |
JOUR |
| author |
Clark, W.E. Saito, M. Vendramin, L. |
| author_facet |
Clark, W.E. Saito, M. Vendramin, L. |
| author_sort |
Clark, W.E. |
| title |
Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| title_short |
Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| title_full |
Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| title_fullStr |
Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| title_full_unstemmed |
Quandle coloring and cocycle invariants of composite knots and abelian extensions |
| title_sort |
quandle coloring and cocycle invariants of composite knots and abelian extensions |
| url |
http://hdl.handle.net/20.500.12110/paper_02182165_v25_n5_p_Clark |
| work_keys_str_mv |
AT clarkwe quandlecoloringandcocycleinvariantsofcompositeknotsandabelianextensions AT saitom quandlecoloringandcocycleinvariantsofcompositeknotsandabelianextensions AT vendraminl quandlecoloringandcocycleinvariantsofcompositeknotsandabelianextensions |
| _version_ |
1807321414155370496 |