22 citations · 79 across the 29 of their papers we have counts for
37 papers
Homological stability fails for the Cremona groups, yet their stable homology is non-trivial
Markus Szymik
The Cremona groups are the groups of all birational transformations of rational varieties, or, in other words, the groups of all automorphisms of rational function fields. These gr…
Artin-Schreier quandles of involutions in absolute Galois groups
Markus Szymik
We introduce a new invariant of fields that refines their real spectrum and is related to their absolute Galois group: the Artin-Schreier quandle. For formally real number fields,…
Generalizations of Loday's assembly maps for Lawvere's algebraic theories
Anna Marie Bohmann, Markus Szymik
Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that…
Groups, conjugation and powers
Markus Szymik, Torstein Vik
We introduce the notion of the power quandle of a group, an algebraic structure that forgets the multiplication but keeps the conjugation and the power maps. Compared with plain qu…
The homotopy types of free racks and quandles
Tyler Lawson, Markus Szymik
We initiate the homotopical study of racks and quandles, two algebraic structures that govern knot theory and related braided structures in algebra and geometry. We prove analogs o…
Preludes to the Eilenberg-Moore and the Leray-Serre spectral sequences
Frank Neumann, Markus Szymik
The Leray-Serre and the Eilenberg-Moore spectral sequences are fundamental tools for computing the cohomology of a group or, more generally, of a space. We describe the relationshi…