Montesinos Amilibia, José MaríaSafont Edo, Carmen2023-06-202023-06-201988-030030-8730https://hdl.handle.net/20.500.14352/57704J. 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.engjournal articlehttp://projecteuclid.org/euclid.pjm/1102689797http://pjm.math.berkeley.edu/open access515.1633-dimensional manifoldsHeegaard splittinglinking formTopología1210 Topología