Two-variable fibrations, factorisation systems and $\infty $ -categories of spans

Autor: Rune Haugseng, Fabian Hebestreit, Sil Linskens, Joost Nuiten

Publikováno v: Forum of Mathematics, Sigma, Vol 11 (2023)

We prove a universal property for $\infty $ -categories of spans in the generality of Barwick’s adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a self-equiva

Externí odkaz: https://doaj.org/article/133992c66b544865b6f4a6384cb5a67d

On the homotopy type of L‐spectra of the integers

Autor: Markus Land, Thomas Nikolaus, Fabian Hebestreit

Publikováno v: Hebestreit, F, Land, M & Nikolaus, T 2021, ' On the homotopy type of L-spectra of the integers ', Journal of Topology, vol. 14, no. 1, pp. 183-214 . https://doi.org/10.1112/topo.12180

We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and a generalised Eilenberg-Mac Lane spectrum. As a consequence, we obtain

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b1f6f08fb6cb75526bc7343268eaba2f
https://doi.org/10.1112/topo.12180

Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces

Autor: Christian Schlichtkrull, Steffen Sagave, Fabian Hebestreit

Publikováno v: Forum of Mathematics Sigma, 8, pp. 1-84
Forum of Mathematics Sigma, 8, 1-84
e16
Forum of Mathematics, Sigma

In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding infinity-categorical product

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e92c75e9706f1727464ddf814751cdc
https://doi.org/10.1017/fms.2020.11

Homotopical and operator algebraic twisted K-theory

Autor: Fabian Hebestreit, Steffen Sagave

Publikováno v: Mathematische Annalen, 378, 1021-1059
Mathematische Annalen, 378, 3-4, pp. 1021-1059

Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the r

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f005bb2c7f597b5f6eb1db6665c757d
http://hdl.handle.net/2066/226231

Cobordism categories and moduli spaces of odd dimensional manifolds

Autor: Nathan Perlmutter, Fabian Hebestreit

We prove that the stable moduli space of $(n-1)$-connected, $n$-parallelizable, $(2n+1)$-dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq 7$. The main novel ingredient is a version of the cobordism category

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19d6e2e5316922daa5c4bbd04f994a27