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Indexed by:期刊论文

Date of Publication:2016-12-01

Journal:INTERNATIONAL JOURNAL OF MATHEMATICS

Included Journals:SCIE、Scopus

Volume:27

Issue:13

ISSN No.:0129-167X

Key Words:3-manifold; Heegaard splitting; intersecting kernel; invariant

Abstract:The intersecting kernel of a Heegaard splitting H1 boolean OR(S) H-2 for a compact orientable 3-manifold M is the subgroup K = Ker(i(1*)) boolean AND Ker(i(2*)) of pi(1)(S), where i(j*) : pi(1)(S) -> pi(1)(H-j) is the homomorphism induced by the inclusion i(j) : S curved right arrow H-j,H- j = 1, 2. In the paper, we obtain some invariants of 3-manifolds M from certain quotient groups of the intersecting kernels of their Heegaard splittings. We also list two algebraic problems related to the new invariants, which might be interesting to study.