16 citations · 81 across the 17 of their papers we have counts for
19 papers
Homology manifolds and euclidean bundles
Fabian Hebestreit, Markus Land, Michael Weiss +1
We construct a Poincaré complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle. This co…
A note on quadratic forms
Fabian Hebestreit, Achim Krause, Maxime Ramzi
For a field extension we consider maps that are quadratic over but whose polarisation is only bilinear over . Our main result is that all such are automatically quadra…
The localisation theorem for the -theory of stable -categories
Fabian Hebestreit, Andrea Lachmann, Wolfgang Steimle
We provide a fairly self-contained account of the localisation and cofinality theorems for the algebraic -theory of stable -categories. It is based on a general…
A short proof of the straightening theorem
Fabian Hebestreit, Gijs Heuts, Jaco Ruit
We provide a short and reasonably self-contained proof of Lurie's straightening equivalence, relating cartesian fibrations over a given -category with contravariant fun…
Stable moduli spaces of hermitian forms
Fabian Hebestreit, Wolfgang Steimle
We prove that Grothendieck-Witt spaces of Poincaré categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Kar…
Mapping spaces in homotopy coherent nerves
Fabian Hebestreit, Achim Krause
We give a direct proof that middle mapping spaces in coherent nerves of Kan enriched categories have the same homotopy type as the original mapping spaces.
Two-variable fibrations, factorisation systems and -categories of spans
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We prove a universal property for -categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the s…
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
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 transformat…
Hermitian K-theory for stable -categories III: Grothendieck-Witt groups of rings
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring to the homotopy -orbits of its K-theory and Ranicki's original (non-period…
Hermitian K-theory for stable -categories II: Cobordism categories and additivity
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We define Grothendieck-Witt spectra in the setting of Poincaré -categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we de…
Hermitian K-theory for stable -categories I: Foundations
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable -categories. Our perspective yields solutions to a varie…
On the homotopy type of L-spectra of the integers
Fabian Hebestreit, Markus Land, Thomas Nikolaus
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…
Connected sum decompositions of high-dimensional manifolds
Imre Bokor, Diarmuid Crowley, Stefan Friedl +4
The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decom…
Homotopical and operator algebraic twisted K-theory
Fabian Hebestreit, Steffen Sagave
Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical a…
Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
Fabian Hebestreit, Steffen Sagave, Christian Schlichtkrull
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 pr…
A vanishing theorem for tautological classes of aspherical manifolds
Fabian Hebestreit, Markus Land, Wolfgang Lück +1
Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational c…
Cobordism categories and moduli spaces of odd dimensional manifolds
Fabian Hebestreit, Nathan Perlmutter
We prove that the stable moduli space of -connected, -parallelizable, -dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq…
Twisted Spin cobordism and positive scalar curvature
Fabian Hebestreit, Michael Joachim
We show how a suitably twisted Spin-cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fund…
The Arone-Goodwillie spectral sequence for and topological realization at odd primes
Sebastian Büscher, Fabian Hebestreit, Oliver Röndigs +1
We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at…