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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Poincaré's cube manifolds

Klaus Volkert

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Abstract

In this article we describe an important class of 3-manifolds studied by Poincaré in his papers on analysis situs (1892 – 1904). They are constructed by identifying the sides of a cube in more or less complicated ways and are therefore called here “cube manifolds”. This idea goes back to Poincarés work on autormorphic functions (early 1880's).

Keywords

cube manifold, history of topology

Mathematical Subject Classification 2010

Primary: 01A55, 01A60

Publication