6 citations · 16 across the 15 of their papers we have counts for
16 papers
The Euler characteristic of manifolds
Renee S. Hoekzema, Luuk Stehouwer, Simona Veselá
We completely determine the possible parities of the Euler characteristic of closed -manifolds of a given dimension. As an application we partially calculate the control…
Super -theory and group completion
David Aretz, Luuk Stehouwer
We develop a spectrum-level graded -theory for real super Banach algebras. Our construction is categorical and homotopy theoretic, in the style of algebraic -theory: the grad…
The many faces of higher Hilbert spaces
Giovanni Ferrer, Lukas Müller, David Penneys +1
Finite-dimensional operator algebras can be viewed as , , or -algebras, leading to different notions for their categories of modules and c…
Unraveling the Bott spiral
Arun Debray, Cameron Krulewski, Luuk Stehouwer
We construct and compute a homotopy-theoretic model for the Bott spiral of symmetry-protected topological phases (SPTs) studied by Queiroz--Khalaf--Stern. We model free and interac…
Free phases of Majorana fermions: Tenfold ways compared
Luuk Stehouwer
We provide a mathematically rigorous classification of symmetry-protected topological (SPT) phases of neutral free fermions. Our approach utilizes Karoubi triples with negative squ…
Is Crane--Yetter fully extended?
Luuk Stehouwer
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifi…
SKK groups of manifolds and non-unitary invertible TQFTs
Renee S. Hoekzema, Luuk Stehouwer, Simona Veselá
This work considers the computation of controllable cut-and-paste groups of manifolds with tangential structure . To this end, we apply the work o…
Weak topological phases in the presence of interactions
Omar Antolín Camarena, Arun Debray, Cameron Krulewski +3
We study weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions. By comparing homotopical free and interacting classifications of these SPTs,…
A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories
Cameron Krulewski, Lukas Müller, Luuk Stehouwer
We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin-statistics theorem. To formulate this extension, we define a `higher spin'…
The spin-statistics theorem for topological quantum field theories
Luuk Stehouwer
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represe…
Dagger -categories
Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd +8
Category theory provides a unified language for organizing composable operations in many disciplines. In disciplines where unitarity is fundamental -- such as functional analysis,…
Dagger categories via anti-involutions and positivity
Luuk Stehouwer, Jan Steinebrunner
Dagger categories are an essential tool for categorical descriptions of quantum physics, for example in categorical quantum mechanics and unitary topological field theory. Their de…
Reflection Structures and Spin Statistics in Low Dimensions
Lukas Müller, Luuk Stehouwer
We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expr…
Some properties of -structures on compact surfaces
Michael R. Klug, Luuk Stehouwer
We show that two -structures on a surface differ by a diffeomorphism of the surface if and only if they are cobordant (for comparison, the analogous fact has al…
Interacting SPT phases are not Morita invariant
Luuk Stehouwer
The tenfold way provides a strong organizing principle for invertible topological phases of matter. Mathematically, it is intimately connected with -theory via the fact that the…
Classification of crystalline topological insulators through K-theory
Luuk Stehouwer, Jan de Boer, Jorrit Kruthoff +1
Topological phases for free fermions in systems with crystal symmetry are classified by the topology of the valence band viewed as a vector bundle over the Brillouin zone. Addition…