Surface mapping classes and Heegaard decompositions of 3-manifolds

Simple item page
dc.contributor.advisorHempel, Johnen_US
dc.creatorLu, Ningen_US
dc.date.accessioned2009-06-04T00:12:50Zen_US
dc.date.available2009-06-04T00:12:50Zen_US
dc.date.issued1990en_US
dc.description.abstractThe thesis is constituted in two parts. The first part including the first four chapters concentrates on the surface mapping class groups. The second part including the last three chapters focuses on their applications in the 3-manifold theory. Chapters I, II, and III show a new set of three generators, L, N and T of the surface mapping class groups ${\cal M}\sb{g}$ and investigate their topological and algebraic properties. Chapter IV finds a finite set of generators of the subgroup ${\cal K}\sb{g},$ which consists of the mapping classes that can be extended to a solid handlebody, in words of the generators of ${\cal M}\sb{g}$ given in the earlier chapters. Chapter V describes all Heegaard decompositions of the 3-sphere, and relates the homology 3-spheres to the elements of the Torelli subgroups. Chapter VI presents a new proof of the fundamental theorem of Kirby calculus on links by using the presentation of ${\cal M}\sb{g}$. The most important result of the thesis, which answers a question asked long ago about the stable equivalence of Heegaard decompositions of 3-manifolds, is proved in Chapter VII. We quote it here: Theorem VII.1.1. Any two Heegaard decompositions of the same genus of a 3-manifold of genus g are stably equivalent by adding no more than 3g - 3 trivial handles.en_US
dc.format.extent236 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Math. 1990 Luen_US
dc.identifier.citationLu, Ning. "Surface mapping classes and Heegaard decompositions of 3-manifolds." (1990) Diss., Rice University. <a href="https://hdl.handle.net/1911/16366">https://hdl.handle.net/1911/16366</a>.en_US
dc.identifier.digitalLuNen_US
dc.identifier.urihttps://hdl.handle.net/1911/16366en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleSurface mapping classes and Heegaard decompositions of 3-manifoldsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LuN.pdf
Size:
11.7 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Rice University Theses and Dissertations