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  4. Actions of Manifold Homeomorphism Groups on Closed Three-Manifolds

Actions of Manifold Homeomorphism Groups on Closed Three-Manifolds

File(s)
Brenner_cornellgrad_0058F_14935.pdf (756.78 KB)
Permanent Link(s)
https://doi.org/10.7298/cy1m-wy68
https://hdl.handle.net/1813/117512
Collections
Cornell Theses and Dissertations
Author
Brenner, Hazel
Abstract

Continuous actions of compact Lie groups on manifolds were extensively studied in the 1950s and 60s. A major milestone was Mostert’s 1957 classification of all such actions with a codimension-one orbit, which, as a corollary, gave a classification (up to equivariant homeomorphism) of all compact Lie group actions - except the circle - on 3-manifolds. Orlik and Raymond completed the picture in 1968 by classifying all circle actions on closed 3-manifolds. More recently, attention has shifted to actions of homeomorphism groups. Despite the deep differences from Lie groups, Militon (2017) classified all actions of Homeo$_0(S^1)$ on the annulus and torus. Chen and Mann (2019) extended this, classifying Homeo$_0(S^1)$-actions on all compact surfaces and developing general tools to study such actions. Using these tools, this dissertation proves a Homeo$_0(M)$ tube theorem and a weak orbit type stratification for actions of manifold homeomorphism groups, offering structural results in analogy with classical Lie group actions.

Description
139 pages
Date Issued
2025-05
Keywords
Continuous group actions
•
Homeomorphism groups
•
Low-dimensional topology
•
Transformation Groups
Committee Chair
Mann, Kathryn
Committee Member
Manning, Jason
Dozier, Benjamin
Degree Discipline
Mathematics
Degree Name
Ph. D., Mathematics
Degree Level
Doctor of Philosophy
Type
dissertation or thesis
Link(s) to Catalog Record
https://newcatalog.library.cornell.edu/catalog/16938382

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