• Corpus ID: 232403992

Bounded cohomology and homotopy colimits

  title={Bounded cohomology and homotopy colimits},
  author={George E. Raptis},
We discuss an approach to the covering and vanishing theorems for the comparison map from bounded cohomology to singular cohomology, based on the observation that the comparison map is the coassembly map for bounded cohomology. 
Bounded acyclicity and relative simplicial volume
We provide new vanishing and glueing results for relative simplicial volume, following up on two current themes in bounded cohomology: The passage from amenable groups to boundedly acyclic groups and
On the simplicial volume and the Euler characteristic of (aspherical) manifolds
. A well-known question by Gromov asks whether the vanishing of the simplicial volume of oriented closed aspherical manifolds implies the vanishing of the Euler characteristic. We study various


Bounded cohomology of amenable covers via classifying spaces
Gromov and Ivanov established an analogue of Leray's theorem on cohomology of contractible covers for bounded cohomology of amenable covers. We present an alternative proof of this fact, using
Notes on the bounded cohomology theory
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects
Topological hypercovers and 1-realizations
Abstract.We show that if U* is a hypercover of a topological space X then the natural map hocolim U* → X is a weak equivalence. This fact is used to construct topological realization functors for the
Simplicial Homotopy Theory
Simplicial sets, model categories, and cosimplicial spaces: applications for homotopy coherence, results and constructions, and more.
Elements of Homotopy Theory
This chapter and the next are adapted from a lecture published in the Proceedings of the Third Physics Workshop, held at the Institute of Theoretical and Experimental Physics, Moscow, in 1975. They
Leray theorems in bounded cohomology theory
The paper is devoted to a generalized and simplified version of author's approach to covering theorems in bounded cohomology theory. The amenability assumptions are replaced by weaker and more
Some characterizations of acyclic maps
  • G. Raptis
  • Mathematics
    Journal of Homotopy and Related Structures
  • 2019
We discuss two categorical characterizations of the class of acyclic maps between spaces. The first one is in terms of the higher categorical notion of an epimorphism. The second one employs the
Homotopy Limit Functors on Model Categories and Homotopical Categories
Model categories: An overview Model categories and their homotopy categories Quillen functors Homotopical cocompleteness and completeness of model categories Homotopical categories: Summary of part
Higher Topos Theory
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the
Gromov's theory of multicomplexes with applications to bounded cohomology and simplicial volume
The simplicial volume is a homotopy invariant of manifolds introduced by Gromov in 1982. In order to study its main properties, Gromov himself initiated the dual theory of bounded cohomology, that