Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-05-01

Journal: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

Included Journals: SCIE

Volume: 146

Page Number: 615-623

ISSN: 0305-0041

Abstract: In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V(1) boolean OR(S1) W(1) for M(1) and V(2) boolean OR(S2) W(2) for M(2) along boundary components F(1) and F(2) under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M(1)) + g(M(2)) - g(F) holds, and another is that under some circumstances we have a better lower bound.