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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Cubical simplicial volume

Clara Löh and Christian Plankl

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Abstract

Cubical simplicial volume is a variation on simplicial volume, based on cubes instead of simplices. Both invariants are homotopy invariants of oriented closed connected manifolds. In this note, we prove that cubical simplicial volume of oriented closed connected surfaces is proportional to ordinary simplicial volume. More precisely, the cubical simplicial volume of an oriented closed connected surface of genus g > 0 is equal to 2g-2.

Keywords

Simplicial volume, cubical singular homology

Mathematical Subject Classification 2010

Primary: 55N10, 57N65

Publication