Remarks On and Around Bounded Differential Forms

Anna Wienhard

Type: Article

Publication Date: 2012-01-01

Citations: 11

DOI: https://doi.org/10.4310/pamq.2012.v8.n2.a5

Abstract

Various exotic cohomology groups can be defined by imposing boundedness conditions on cochains.This note discusses what happens if we impose boundedness conditions in the standard deRham complex of differential forms on a Riemannian manifold and surveys relations of the resulting bounded deRham cohomology to bounded cohomology and l ∞ -cohomology.

Locations

Pure and Applied Mathematics Quarterly - View - PDF

Similar Works

Action	Title	Year	Authors
+	Bounded cohomology and negatively curved manifolds	2011	Sungwoon Kim Инканг Ким
+	Bounded differential forms and coinvariants of bounded functions	2023	Francesco Milizia
+ PDF Chat	Bounded cohomology classes of exact forms	2023	Ludovico Battista Stefano Francaviglia Marco Moraschini Filippo Sarti Alessio Savini
+	Some Remarks on Bounded Cohomology	1981	Robert Brooks
+	Bounded Cohomology Classes of Exact Forms	2022	Ludovico Battista Stefano Francaviglia Marco Moraschini Filippo Sarti Alessio Savini
+	An introduction to bounded cohomology	2008	Michelle Bucher
+	On the algebraic foundations of bounded cohomology	2011	Theo Bühler
+ PDF Chat	Low-dimensional bounded cohomology and extensions of groups	2020	Nicolaus Heuer
+	On the Algebraic Foundation of Bounded Cohomology	2008	EidgenTechnische Hochschule Z
+	Differential Geometry on Complex and Almost Complex Spaces.	1967	A. L. Hilt Kentaro Yano
+	Manifolds of Bounded Geometry	2013	Jaap Eldering
+	On and Around the Bounded Cohomology of SL2	2002	Marc Burger Nicolas Monod
+	Differential geometry on complex and almost complex spaces	1965	健太郎矢野
+	Notes on the bounded cohomology theory	2017	Nikolai V. Ivanov
+	On 3-dimensional Bounded Cohomology of Surfaces	2018	Tomoyoshi Yoshida
+	Curvature, bounded cohomology and path integrals	2001	Lo Yang Shing‐Tung Yau
+	Dirac cohomology on manifolds with boundary and spectral lower bounds	2023	Simone Farinelli
+	Bounded cohomology of transformation groups	2019	Michael Brandenbursky Michał Marcinkowski
+	Bounded cohomology of transformation groups	2019	Michael Brandenbursky Michał Marcinkowski
+ PDF Chat	Bounded cohomology of diffeomorphism groups of higher dimensional spheres	2024	Zixiang Zhou

Works That Cite This (11)

Action	Title	Year	Authors
+ PDF Chat	Hyperbolicity and bounded-valued cohomology	2024	Nansen Petrosyan Vladimir Vankov
+ PDF Chat	Hierarchically cocompact classifying spaces for mapping class groups of surfaces	2018	Brita E. A. Nucinkis Nansen Petrosyan
+	Bounded cohomology and the Cheeger isoperimetric constant	2015	Sungwoon Kim Инканг Ким
+ PDF Chat	Complete Bredon cohomology and its applications to hierarchically defined groups	2016	Brita E. A. Nucinkis Nansen Petrosyan
+ PDF Chat	Signed quasiregular curves	2023	Susanna Heikkilä
+	Classifying spaces with virtually cyclic stabilisers for certain infinite cyclic extensions	2011	Martin Fluch
+	Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov	2022	Dario Ascari Francesco Milizia
+ PDF Chat	Central extensions and bounded cohomology	2023	Roberto Frigerio Alessandro Sisto
+ PDF Chat	Volumes of SLn(ℂ)–representations of hyperbolic 3–manifolds	2018	Wolfgang Pitsch Joan Porti
+ PDF Chat	Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov	2024	Dario Ascari Francesco Milizia

Works Cited by This (17)

Action	Title	Year	Authors
+	Continuous Bounded Cohomology of Locally Compact Groups	2014	Nicolas Monod
+	Asymptotic invariants of infinite groups	1993	Mikhael Gromov Graham A. Niblo Martin A. Roller
+	Geometric Integration Theory	1957	Hassler Whitney
+ PDF Chat	Growth of maps, distortion in groups and symplectic geometry	2002	Leonid Polterovich
+ PDF Chat	A Vanishing Theorem for the Tangential de Rham Cohomology of a Foliation with Amenable Fundamental Groupoid	2004	Kevin Corlette Luis Hernández Lamoneda Alessandra Iozzi
+ PDF Chat	Hermitian symmetric spaces and Kahler rigidity	2007	Marc Burger Alessandra Iozzi Anna Wienhard
+	Cohomological lower bounds for isoperimetric functions on groups	1998	S. M. Gersten
+ PDF Chat	Bounded Kähler class rigidity of actions on Hermitian symmetric spaces	2004	M. Burger Alessandra Iozzi
+	Straightening and bounded cohomology of hyperbolic groups	2001	Igor Mineyev
+ PDF Chat	Simplical volume of closed locally symmetric spaces of non-compact type	2006	Jean-François Lafont Benjamin Schmidt