4 papers
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,…
The homology of permutation racks
Victoria Lebed, Markus Szymik
Despite a blossoming of research activity on racks and their homology for over two decades, with a record of diverse applications to central parts of contemporary mathematics, ther…
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…
Homological stability fails for the Cremona groups
Markus Szymik
The Cremona groups are the groups of all birational equivalences of rational varieties and, equivalently, the automorphism groups of the rational function fields. In this note, we…