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Poincaré's cube manifolds

Klaus Volkert


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).


cube manifold, history of topology

Mathematical Subject Classification 2010

Primary: 01A55, 01A60


Received: 11th November 2012
Accepted: 12th February 2013
Published: 13th May 2013
Editor: Erhard Scholz