Zobrazeno 1 - 10
of 180
pro vyhledávání: '"SZYMIK, MARKUS"'
Autor:
Szymik, Markus
We reveal that Thompson's group $F$ has a quandle refinement, and we establish some essential results about the originating quandle.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/2407.06058
Autor:
Szymik, Markus
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 explain that homological stability fails for them in both possible way
Externí odkaz:
http://arxiv.org/abs/2403.07546
Autor:
Szymik, Markus
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, it is freely generated in its variety by a Cantor space of indetermina
Externí odkaz:
http://arxiv.org/abs/2403.07545
Autor:
Bohmann, Anna Marie, Szymik, Markus
Publikováno v:
J. Inst. Math. Jussieu 23 (2024) 811--837
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 places both ingredients on the same footing. Building on Elmendorf--Ma
Externí odkaz:
http://arxiv.org/abs/2112.07003
Autor:
Szymik, Markus, Vik, Torstein
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 quandles, power quandles are much better invariants of groups. We show t
Externí odkaz:
http://arxiv.org/abs/2111.08998
Autor:
Neumann, Frank, Szymik, Markus
Publikováno v:
Doc. Math. 29 (2024) 1319-1339
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 relationship between these two spectral sequences when both of them share the sam
Externí odkaz:
http://arxiv.org/abs/2106.10209
Autor:
Lawson, Tyler, Szymik, Markus
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 of Milnor's theorem on free groups for these theories and their pointed
Externí odkaz:
http://arxiv.org/abs/2106.01299
Autor:
Bohmann, Anna Marie, Szymik, Markus
Publikováno v:
Math. Proc. Camb. Phil. Soc. 175 (2023) 253-270
The algebraic K-theory of Lawvere theories is a conceptual device to elucidate the stable homology of the symmetry groups of algebraic structures such as the permutation groups and the automorphism groups of free groups. In this paper, we fully addre
Externí odkaz:
http://arxiv.org/abs/2011.11755
Autor:
Lebed, Victoria, Szymik, Markus
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, there are still very few examples of racks whose homology has been fully c
Externí odkaz:
http://arxiv.org/abs/2011.04524
Autor:
Szymik, Markus
Publikováno v:
J. Algebra 324 (2010) 2589-2593
The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important role in representation theory, and their groups
Externí odkaz:
http://arxiv.org/abs/2002.04878