Volume 33, Issue 3
On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems

Commun. Math. Res., 33 (2017), pp. 215-222.

Published online: 2019-11

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• Abstract

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ∂-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ∂-reducible 3-manifold M with one boundary component F of genus $n > 0$ which admits a complete surface system S′ , if D is a collection of pairwise disjoint compression disks for ∂M, then there exists a complete surface system S for M, which is equivalent to S′ , such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S3.

• Keywords

complete surface system, ∂-reducibility, Heegaard splitting

57M25, 55Q20

zhaoyan jinzh@126.com (Yan Zhao)

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@Article{CMR-33-215, author = {Yan and Zhao and zhaoyan jinzh@126.com and 5414 and School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 and Yan Zhao and Fengchun and Lei and and 5415 and School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 and Fengchun Lei and Fengling and Li and and 5416 and School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 and Fengling Li}, title = {On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {33}, number = {3}, pages = {215--222}, abstract = {

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ∂-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ∂-reducible 3-manifold M with one boundary component F of genus $n > 0$ which admits a complete surface system S′ , if D is a collection of pairwise disjoint compression disks for ∂M, then there exists a complete surface system S for M, which is equivalent to S′ , such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S3.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.03.03}, url = {http://global-sci.org/intro/article_detail/cmr/13377.html} }
TY - JOUR T1 - On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems AU - Zhao , Yan AU - Lei , Fengchun AU - Li , Fengling JO - Communications in Mathematical Research VL - 3 SP - 215 EP - 222 PY - 2019 DA - 2019/11 SN - 33 DO - http://doi.org/10.13447/j.1674-5647.2017.03.03 UR - https://global-sci.org/intro/article_detail/cmr/13377.html KW - complete surface system, ∂-reducibility, Heegaard splitting AB -

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ∂-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ∂-reducible 3-manifold M with one boundary component F of genus $n > 0$ which admits a complete surface system S′ , if D is a collection of pairwise disjoint compression disks for ∂M, then there exists a complete surface system S for M, which is equivalent to S′ , such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S3.

Yan Zhao, Feng-chun Lei & Fengling Li. (2019). On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems. Communications in Mathematical Research . 33 (3). 215-222. doi:10.13447/j.1674-5647.2017.03.03
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