22 citations · 79 across the 29 of their papers we have counts for
5 papers · 1 filter
Quandle cohomology is a Quillen cohomology
Markus Szymik
We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectivel…
Alexander-Beck modules detect the unknot
Markus Szymik
We introduce the Alexander-Beck module of a knot as a canonical refinement of the classical Alexander module, and we prove that this new invariant is an unknot-detector.
Permutations, power operations, and the center of the category of racks
Markus Szymik
Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quan…
The rational stable homology of mapping class groups of universal nil-manifolds
Markus Szymik
We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers an…
Spectral sequences for Hochschild cohomology and graded centers of derived categories
Frank Neumann, Markus Szymik
The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristi…