22 citations · 79 across the 29 of their papers we have counts for
9 papers · 1 filter
Boolean algebras, Morita invariance, and the algebraic K-theory of Lawvere theories
Anna Marie Bohmann, Markus Szymik
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 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…
A stable approach to the equivariant Hopf theorem
Markus Szymik
Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner, the homotopy classes of G-equivariant maps into a G-sphere are described in terms of th…
K3 spectra
Markus Szymik
The notion of a K3 spectrum is introduced in analogy with that of an elliptic spectrum and it is shown that there are "enough" K3 spectra in the sense that for all K3 surfaces X in…
The Brauer group of Burnside rings
Markus Szymik
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 gro…
The chromatic filtration of the Burnside category
Markus Szymik
The Segal map connects the Burnside category of finite groups to the stable homotopy category of their classifying spaces. The chromatic filtrations on the latter can be used to de…
Bauer--Furuta invariants and Galois symmetries
Markus Szymik
The Bauer-Furuta invariants of smooth 4-manifolds are investigated from a functorial point of view. This leads to a definition of equivariant Bauer-Furuta invariants for compact Li…
Characteristic cohomotopy classes for families of 4-manifolds
Markus Szymik
Families of smooth closed oriented 4-manifolds with a complex spin structure are studied by means of a family version of the Bauer--Furuta invariants in the context of parametrised…
Stable diffeomorphism groups of 4-manifolds
Markus Szymik
A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen n-manifold Y. On the level of automorphism groups, th…