Categories of diagrams with irreversible moves
AbstractWe work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition regarding the existence of certain morphisms in an associated category is satisfied for every move of the sequence. This conditional setting leads to a possibility of irreversible moves, terminal states, and to using functors more general than the ones used as knot invariants. Our main focus is the category of diagrams with a binary relation on the set of arcs, indicating which arc can move over another arc. We define homology of binary relations, and merge it with quandle homology, to obtain the homology for partial quandles with a binary relation. This last homology can be used to analyze link diagrams with a binary relation on the set of components.
|Journal series||Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, (A 20 pkt)|
|Publication size in sheets||1.45|
|Keywords in English||conditional knot theory, irreversible move, homology of a binary relation, indicator, rack homology|
|Score||= 20.0, 30-09-2019, ArticleFromJournal|
|Publication indicators||: 2016 = 0.786; : 2017 = 0.458 (2) - 2017=0.562 (5)|
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