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

Yan Zhao, Fengchun Lei & Fengling Li

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

  • AMS Subject Headings

57M25, 55Q20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhaoyan jinzh@126.com (Yan Zhao)

  • BibTex
  • RIS
  • TXT
@Article{CMR-33-215, author = {Zhao , Yan and Lei , Fengchun and Li , Fengling}, 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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