Homology Curve Complex

DOI: 10.4236/apm.2012.22017   PDF   HTML     2,913 Downloads   6,457 Views  

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).

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N. Singh and H. Mukerjee, "Homology Curve Complex," Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 119-123. doi: 10.4236/apm.2012.22017.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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