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

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

Journal

Science China Mathematics
ISSN: 1674-7283 , E-ISSN: 1869-1862

Output data

Year: 2020, Volume: 2020, Number: 63, Pages: 1997-2004 Pages count : 8 DOI: 10.1007/s11425-019-1647-9

Tags

57N10; free group; handlebody; surface sum of 3-manifolds

Authors

Lei Fengchun ¹ , Liu He ¹ , Li Fenglinf ¹ , Vesnin A. ²

Affiliations

1	Dalian University of Technology
2	Regional Scientific and Educational Mathematical Center, Department of Mechanics and Mathematics, Tomsk State University, Tomsk, 634050, Russia

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.

Lei F. , Liu H. , Li F. , Vesnin A.
A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody
Science China Mathematics. 2020. V.2020. N63. P.1997-2004. DOI: 10.1007/s11425-019-1647-9 WOS Scopus OpenAlex

Web of science:	WOS:000521674100001
Scopus:	2-s2.0-85082176953
OpenAlex:	W3013000767

DB	Citing
Scopus	5
OpenAlex	5
Web of science	6