• Corpus ID: 245131273

Generalizations of Loday's assembly maps for Lawvere's algebraic theories

@inproceedings{Bohmann2021GeneralizationsOL,
  title={Generalizations of Loday's assembly maps for Lawvere's algebraic theories},
  author={Anna Marie Bohmann and Markus Szymik},
  year={2021}
}
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–Mandell’s multiplicativity results and our earlier work, we show that the K-theory of Lawvere theories is lax monoidal. This result makes it possible to present our theory in a user-friendly way without using higher categorical language. It also allows… 
View PDF on arXiv
1 Citations

One Citation

Boolean algebras, Morita invariance, and the algebraic K-theory of Lawvere theories
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…

References

SHOWING 1-10 OF 54 REFERENCES
Segal’s Gamma rings and universal arithmetic
Segal's Gamma-rings provide a natural framework for absolute algebraic geometry. We use Almkvist's global Witt construction to explore the relation with J. Borger F1-geometry and compute the Witt…
Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory.
We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of…
The cyclotomic trace and algebraic K-theory of spaces
The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, and…
The cyclotomic trace and the K-theoretic analogue of Novikov's conjecture.
TLDR
The cyclotomic trace detects the Borel classes in algebraic K-theory of the integers, and is used to prove, for a wide class of groups, that the K- theoretic assembly map is rationally injective.
Rings, modules, and algebras in infinite loop space theory
Absolute algebra and Segal's Γ-rings: Au dessous de Spec(Z)‾
Boolean algebras, Morita invariance, and the algebraic K-theory of Lawvere theories
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…
Presentations of generalisations of Thompson’s group V
We consider generalisations of Thompson's group $V$, denoted by $V_r(\Sigma)$, which also include the groups of Higman, Stein and Brin. It was shown by the authors in [20] that under some mild…
Bredon cohomological finiteness conditions for generalisations of Thompson's groups
We define a family of groups that generalises Thompson's groups $T$ and $G$ and also those of Higman, Stein and Brin. For groups in this family we descrine centralisers of finite subgroups and show,…
New Approach to Arakelov Geometry
This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct…
...
...