MARC details
| 000 -LEADER |
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| fixed length control field |
02717ntm a22003977a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
AT-ISTA |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20201014130003.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
201014s2020 au ||||| m||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Transcribing agency |
IST |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Huszar, Kristof |
| 9 (RLIN) |
216832 |
| 245 ## - TITLE STATEMENT |
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| Title |
Combinatorial width parameters for 3-dimensional manifolds |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc. |
IST Austria |
| Date of publication, distribution, etc. |
2020 |
| 500 ## - GENERAL NOTE |
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| General note |
Thesis |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Abstract |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Acknowledgments |
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About the Author |
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| Formatted contents note |
List of Publications |
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List of Tables |
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List of Figures |
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| Formatted contents note |
1 Introduction |
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2 Preliminaries on Graphs and Parameterized Complexity |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
3 A Primer on 3-Manifolds |
| 505 ## - FORMATTED CONTENTS NOTE |
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4 Interfaces between Combinatorics and Topology |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
5 From Combinatorics to Topology and Back – In a Quantitative Way |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
6 The Classification of 3-Manifolds with Treewidth One |
| 505 ## - FORMATTED CONTENTS NOTE |
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7 Some 3-Manifolds with Treewidth Two |
| 505 ## - FORMATTED CONTENTS NOTE |
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Appendix A Computational Aspects |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Appendix B High-Treewidth Triangulations |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Appendix C The 1-Tetrahedron Layered Solid Torus |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Appendix D An Algorithmic Aspect of Layered Triangulations |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Appendix E Generating Treewidth Two Triangulations Using Regina |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Bibliography |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.” In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.15479/AT:ISTA:8032">https://doi.org/10.15479/AT:ISTA:8032</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |