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Oleg Viro


This is hopefully a complete account of the topology of 1-dimensional manifolds. In general, this material is not well represented in the literature. This probably happened because it is considered too simple. Hence it is difficult to find appropriate references. The proofs are very simple, but use ideas that are less applicable in similar high-dimensional situations. This is why most the results below are provided with proofs.


1-manifold, topological classification, orientation, group of self-homeomorphisms, mapping class group, finite group actions, intrinsic metric

Mathematical Subject Classification 2010

Primary: 57-00, 57-01, 57M99, 57N16, 57R99, 57S10, 57S17, 57S25


Received: 5th February 2013
Revised: 14th May 2013
Accepted: 28th May 2013
Editor: Peter Landweber