Two-variable fibrations, factorisation systems and-categories of spans
R Haugseng, F Hebestreit, S Linskens… - Forum of Mathematics …, 2023 - cambridge.org
Two-variable fibrations, factorisation systems and ∞-categories of spans Page 1 Forum of
Mathematics, Sigma (2023), Vol. 11:e111 1–70 doi:10.1017/fms.2023.107 RESEARCH ARTICLE …
Mathematics, Sigma (2023), Vol. 11:e111 1–70 doi:10.1017/fms.2023.107 RESEARCH ARTICLE …
Stable moduli spaces of hermitian forms
F Hebestreit, W Steimle - arXiv preprint arXiv:2103.13911, 2021 - arxiv.org
We prove that Grothendieck-Witt spaces of Poincar\'e categories are, in many cases, group
completions of certain moduli spaces of hermitian forms. This, in particular, identifies …
completions of certain moduli spaces of hermitian forms. This, in particular, identifies …
Lax monoidal adjunctions, two‐variable fibrations and the calculus of mates
R Haugseng, F Hebestreit, S Linskens… - Proceedings of the …, 2023 - Wiley Online Library
We provide a calculus of mates for functors to the∞ ∞‐category of∞ ∞‐categories and
extend Lurie's unstraightening equivalences to show that (op) lax natural transformations …
extend Lurie's unstraightening equivalences to show that (op) lax natural transformations …
On the rational motivic homotopy category
We study the structure of the rational motivic stable homotopy category over general base
schemes. Our first class of results concerns the six operations: we prove absolute purity …
schemes. Our first class of results concerns the six operations: we prove absolute purity …
Simple homotopy invariance of the loop coproduct
F Naef, P Safronov - arXiv preprint arXiv:2406.19326, 2024 - arxiv.org
We prove a transformation formula for the Goresky-Hingston loop coproduct in string
topology under homotopy equivalences of manifolds. The formula involves the trace of the …
topology under homotopy equivalences of manifolds. The formula involves the trace of the …
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
R Haugseng, F Hebestreit, S Linskens… - arXiv preprint arXiv …, 2020 - arxiv.org
We provide a calculus of mates for functors to the $\infty $-category of $\infty $-categories
and extend Lurie's unstraightening equivalences to show that (op) lax natural …
and extend Lurie's unstraightening equivalences to show that (op) lax natural …
On the parametrized Tate construction
JD Quigley, J Shah - arXiv preprint arXiv:2110.07707, 2021 - arxiv.org
We introduce and study a genuine equivariant refinement of the Tate construction
associated to an extension $\widehat {G} $ of a finite group $ G $ by a compact Lie group …
associated to an extension $\widehat {G} $ of a finite group $ G $ by a compact Lie group …
Torsion volume forms
F Naef, P Safronov - arXiv preprint arXiv:2308.08369, 2023 - arxiv.org
We introduce volume forms on mapping stacks in derived algebraic geometry using a
parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks …
parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks …
On the homotopy type of L‐spectra of the integers
F Hebestreit, M Land, T Nikolaus - Journal of Topology, 2021 - Wiley Online Library
We show that quadratic and symmetric L‐theory of the integers are related by Anderson
duality and that both spectra split integrally into the L‐theory of the real numbers and a …
duality and that both spectra split integrally into the L‐theory of the real numbers and a …
A motivic spectrum representing hermitian K-theory
B Calmès, Y Harpaz, D Nardin - arXiv preprint arXiv:2402.15136, 2024 - arxiv.org
We establish fundamental motivic results about hermitian K-theory without assuming that 2
is invertible on the base scheme. In particular, we prove that both quadratic and symmetric …
is invertible on the base scheme. In particular, we prove that both quadratic and symmetric …