Contents - 2017

• Cubical simplicial volume
  Clara Löh and Christian Plankl
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• Brouwer degree, domination of manifolds, and groups presentable by products
  Pierre de la Harpe
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Contents - 2014

• Poincaré's conjecture
  Klaus Volkert
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Contents - 2013

• Fake lens spaces
  Tibor Macko
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• Lens spaces in dimension three: a history
  Klaus Volkert
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• Poincaré's cube manifolds
  Klaus Volkert
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• Poincaré's homology sphere
  Klaus Volkert
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• Projective plane: a history
  Klaus Volkert
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• Space forms: a history
  Klaus Volkert
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• 1-manifolds
  Oleg Viro
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Contents - 2012

• Aspherical manifolds
  Wolfgang Lück
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Contents - 2011

• Super manifolds: an incomplete survey
  Henning Hohnhold, Stephan Stolz and Peter Teichner
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• Simplicial volume
  Clara Löh
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• Hirzebruch surfaces
  Diarmuid Crowley and Matthias Kreck
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• Bordism
  Taras Panov
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• Complex bordism
  Taras Panov
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• Formal group laws and genera
  Taras Panov
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• 5-manifolds: 1-connected
  Diarmuid Crowley
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Simplicial volume

Clara Löh

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Abstract

Simplicial volume is a homotopy invariant of oriented closed connected manifolds introduced by Gromov in his proof of Mostow rigidity. On the one hand, the simplicial volume of a Riemannian manifold encodes non-trivial information about the Riemannian volume; on the other hand, simplicial volume can be described in terms of a certain functional analytic version of homological algebra (bounded cohomology). In this article we survey important properties and applications of simplicial volume as well as useful techniques for working with simplicial volume.

Keywords

simplicial volume, minimal volume, bounded cohomology

Mathematical Subject Classification 2010

Primary: 53C23, 57R99

Publication