Abstract/Details

Normal surfaces in fibered 3-manifolds

Wang, Ningyi. 
 University of Connecticut ProQuest Dissertations Publishing,  1992. 9310273.

Abstract (summary)

Let M be a connected, compact 3-manifold with a fixed triangulation $\cal T$. There is a linear system, called the system of matching equations, associated with $\cal T$. A normal surface, a properly immersed surface which intersects each tetrahedron of $\cal T$ nicely, corresponds to a non-negative integral solution to the system of matching equations. A non-negative integral solution to the system of matching equations is called admissible is there is a normal surface corresponding to it. The system of normal equations is obtained by adding the normalizing equation to the system of matching equations. The space of solutions to the system normal equations is a convex cell in $R\sp{n}$ and is called the projective solution space of M associated with $\cal T$.

In this thesis we give necessary and sufficient conditions to determine if a non-negative integral solution to the system of matching equations is admissible. We also study the projective solution spaces of 3-manifolds which fibers over $S\sp1$. At last we characterize certain kind incompressible surfaces properly embedded in F $\times$ I, where F is an orientable, closed surface.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; three-manifolds
Title
Normal surfaces in fibered 3-manifolds
Author
Wang, Ningyi
Number of pages
76
Degree date
1992
School code
0056
Source
DAI-B 53/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-208-16466-2
Advisor
Tollefson, Jeffery
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9310273
ProQuest document ID
303977108
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303977108/abstract