On rack cohomology
Copyright policy )On rack cohomology
We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomology given by Carter, Jelsovsky, Kamada, and Saito, are in fact equalities. We compute as well the Betti numbers of the twisted cohomology introduced by Carter, Elhamdadi, and Saito. We also give a group-theoretical interpretation of the second cohomology group for racks.
Boundary formula corrected. 9 pages
- Massachusetts Institute of Technology United States
quandles, Algebra and Number Theory, rack cohomology, Invariants of knots and \(3\)-manifolds, cohomology groups, Other homology theories in algebraic topology, Hopf algebras (associative rings and algebras), racks, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Betti numbers, Cohomology of groups, Other (co)homology theories
quandles, Algebra and Number Theory, rack cohomology, Invariants of knots and \(3\)-manifolds, cohomology groups, Other homology theories in algebraic topology, Hopf algebras (associative rings and algebras), racks, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Betti numbers, Cohomology of groups, Other (co)homology theories
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).41 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!