Heegaard splittings of the Brieskorn homology spheres that are equivalent after one stabilization


We construct a class of 3-manifolds M_q which are homeomorphic to  the Brieskorn homology spheres \sum(2,3,q), where (2,3,q) are  relatively prime. Also, we show that M_q is a 2-fold cyclic  branched covering of S^3 over a knot K_q which is inequivalent  with torus knot T(3,q) for q \ge 7. Moreover, we show that two  inequivalent Heegaard splittings of \sum(2,3,q) of genus 2  associated with T(3,q) and K_q are equivalent after single  stabilization.

DOI Code: 10.1285/i15900932v20n1p53

Keywords: Crystallization; Heegaard splitting; Crystallization move; Brieskorn homology sphere

Classification: 57M12; 57M15; 57M50

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