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On the Birman invariants of Heegaard splittings

Montesinos Amilibia, José María and Safont Edo, Carmen (1988) On the Birman invariants of Heegaard splittings. Pacific Journal of Mathematics, 132 (1). pp. 113-142. ISSN 0030-8730

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Abstract

J. Birman had observed that the homological information about a given Heegaard splitting of genus g is contained in a double coset in the group of symplectic 2g×2g integer matrices with respect to a suitable subgroup, and found a determinant invariant of this double coset. We obtain complete invariants of these double cosets by characterizing it in terms of the linking form of the manifold lifted to a handlebody of the Heegaard splitting and then finding complete invariants of this lifted form.

Item Type:Article
Uncontrolled Keywords:3-dimensional manifolds; Heegaard splitting; linking form
Subjects:Sciences > Mathematics > Topology
ID Code:17092
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