Amenable covers and integral foliated simplicial volume

In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical n-manifolds that admit an open amenable cover of multiplicity at most n is zero. This implies that the fundamental groups of such manifolds have fixed price and are cheap as well as reproves some statements about homology growth

The HERMIT in the machine: a plugin for the interactive transformation of GHC core language programs

The importance of reasoning about and refactoring programs is a central tenet of functional programming. Yet our compilers and development toolchains only provide rudimentary support for these tasks. This paper introduces a programmatic and compiler-centric interface that facilitates refactoring and equational reasoning. To develop our ideas, we have implemented HERMIT, a toolkit enabling informal but systematic transformation of Haskell programs from inside the Glasgow Haskell Compiler’s optimization pipeline. With HERMIT, users can experiment with optimizations and equational reasoning, while the tedious heavy lifting of performing the actual transformations is done for them. HERMIT provides a transformation API that can be used to build higher-level rewrite tools. One use-case is prototyping new optimizations as clients of this API before being committed to the GHC toolchain. We describe a HERMIT application - a read-eval-print shell for performing transformations using HERMIT. We also demonstrate using this shell to prototype an optimization on a specific example, and report our initial experiences and remaining challenges

l 1 -homology and simplicial volume:l1-homology and simplicial volume

Vervollständigen und Dualisieren des singulären Kettenkomplexes bezüglich der l1-Norm führt zu l1-Homologie bzw. beschränkter Kohomologie. Im Gegensatz zu l1-Homologie ist beschränkte Kohomologie durch die Arbeiten von Gromov und Ivanov gut verstanden. Wir entwickeln eine Methode, die es erlaubt Isomorphismen auf Homologie von Banach-Kettenkomplexen in Isomorphismen auf Kohomologie der dualen Komplexe zu übersetzen und umgekehrt. Daher können wir gewisse Resultate über beschränkte Kohomologie in entsprechende Resultate über l1-Homologie transformieren. Zum Beispiel erhalten wir einen neuen, einfachen Beweis dafür, daß l1-Homologie nur von der Fundamentalgruppe abhängt und daß l1-Homologie eine Beschreibung durch projektive Auflösungen besitzt. Im zweiten Teil der Arbeit werden Anwendungen von l1-Homologie auf das simpliziale Volumen nicht-kompakter Mannigfaltigkeiten studiert. Taking the l1-completion and the topological dual of the singular chain complex gives rise to l1-homology and bounded cohomology respectively. Unlike l1-homology, bounded cohomology is quite well understood by the work of Gromov and Ivanov. We derive a mechanism linking isomorphisms on the level of homology of Banach chain complexes to isomorphisms on the level of cohomology of the dual Banach cochain complexes and vice versa. Therefore, certain results on bounded cohomology can be transferred to l1-homology. For example, we obtain a new, simple proof of the fact that l1-homology depends only on the fundamental group and that l1-homology with twisted coefficients admits a description in terms of projective resolutions. In the second part, we study applications of l1-homology concerning the simplicial volume of non-compact manifolds

Median quasimorphisms on CAT(0) cube complexes and their cup products

Acknowledgements: We wish to thank Matthew Cordes, Talia Fernós, Elia Fioravanti and Nicolas Monod for helpful discussions, as well as Sofia Amontova, Michelle Bucher, and Marco Moraschini for discussions on cup products and Lex. Moreover, we would like to thank Franziska Hofmann for spotting a gap in an earlier version of this paper, and the anonymous referee for several helpful comments, including a fix of the gap.Funder: Herchel Smith Postdoctoral Fellowship FundAbstractCup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on $${{\,\mathrm{{CAT}}\,}}(0)$$ CAT ( 0 ) cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology.</jats:p

Generics as a Library

A generic function is a function that is defined on the structure of data types: with a single definition, we obtain a function that works for many data types. In contrast, an ad-hoc polymorphic function requires a separate implementation for each data type. Previous work by Hinze on lightweight generic programming has introduced techniques that allow the definition of generic functions directly in Haskell

Generics as a Library (Extended Abstract)

Typically, a generic function is a function that is defined on the structure of data types: with a single definition, we obtain a function that works for many data types. In contrast, an ad-hoc polymorphic function requires a separate implementation for each data type. Previous work by Hinze on lightweight generic programming has introduced techniques that allow the definition of generic functions directly in Haskell