Author(s)

Ningthoujam Jiban Singh, Himadri Kumar Mukerjee

Department of Mathematics, Assam University, Silchar, India.
Department of Mathematics, North-Eastern Hill University, NEHU Campus, Shillong, India.

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).

Homology Curve Complex; Heegaard Splittings; Incompressible Surface

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.