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J. Birman, “The Topology of 3-Manifolds, Heegaard Distances and the Mapping Class Group of a 2-Manifold,” arXiv.org, 2005. http://arxiv.org/abs/math/0502545

has been cited by the following article:

• TITLE: Homology Curve Complex

  AUTHORS: Ningthoujam Jiban Singh, Himadri Kumar Mukerjee

  KEYWORDS: Homology Curve Complex; Heegaard Splittings; Incompressible Surface

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.2, March 22, 2012

  ABSTRACT: A homological analogue of curve complex of a closed connected orientable surface is developed and studied. The dis-tance in this complex is shown to be quite computable and an algorithm given (Theorem 3.5). As an application of this complex it is shown that for a closed orientable 3-manifold, and any of its Heegaard splittings, one can give an algorithm to decide whether the manifold contains a 2-sided, non-separating, closed incompressible surface (Theorem 1.1).