A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody

Autor: Andrei Vesnin, Fengling Li, He Liu, Fengchun Lei
Rok vydání: 2020
Předmět:
Zdroj: Science China Mathematics. 63:1997-2004
ISSN: 1869-1862
1674-7283
Popis: The main results of the paper are that we give a necessary and sufficient condition for a surface sum of two handlebodies along a connected surface to be a handlebody as follows: (1) The annulus sum H = H1∪AH2 of two handlebodies H1 and H2 is a handlebody if and only if the core curve of A is a longitude for either H1 or H2; (2) Let H = H1∪Sg,b H2 be a surface sum of two handlebodies H1 and H2 along a connected surface S = Sg,b,,b ≥ 1, ni = g(Hi) ≥ 2, i = 1, 2. Suppose that S is incompressible in both H1 and H2. Then H is a handlebody if and only if there exists a basis J = {J}1,…, Jm with a partition (J1, J2) of J such that J1 is primitive in H1 and J2 is primitive in H2.
Databáze: OpenAIRE
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