Abstract/Details

Decision algorithms and normal surfaces in 3-manifolds

Boman, Margaret Ann. 
 University of Connecticut ProQuest Dissertations Publishing,  1990. 9119504.

Abstract (summary)

The normal system of equations ${\cal N}$(M,${\cal T}$) is derived for a closed, irreducible 3-manifold M having a fixed triangulation ${\cal T}$. Corresponding to each normal surface F, a branched normal surface $B\sb{F}$ is constructed. We show that to determine whether M is Haken, it is sufficient to test the set of branched normal surfaces $B\sb{F}$ associated with the finite set of vertex surfaces F of (M,${\cal T}$) for injectivity. If some $B\sb{F}$ is found to be injective then M is Haken.

We produce an algorithm to test a branched surface $B\sb{F}$ for injectivity. It is shown that if there is an essential punctured compression disk or an essential punctured monogon then such a disk will exist as a vertex surface of ${\cal N}(M\sb\sigma$,${\cal T}\sb\sigma)$, where $M\sb\sigma$ = Cl($M - N(B\sb{F}))$.

A system of equations which is equivalent on admissible vertices to the normal Q-system is found. Computer programs to implement these algorithms were written in connection with this paper.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; three-manifolds
Title
Decision algorithms and normal surfaces in 3-manifolds
Author
Boman, Margaret Ann
Number of pages
77
Degree date
1990
School code
0056
Source
DAI-B 52/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-207-40427-1
Advisor
Tollefson, Jeffrey L.
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
9119504
ProQuest document ID
303844791
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303844791/abstract