The fundamental surgery theorem and the classification of manifolds
The purpose of this paper is to present a survey of some important results in the classification of differentiable manifolds. We begin with the Poincaré conjecture and its partial solution using the h-cobordism theorem. We review next the work of Kervaire and Milnor, concerned with the diffeomorphis...
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ndltd-UBC-oai-circle.library.ubc.ca-2429-224692018-01-05T17:41:41Z The fundamental surgery theorem and the classification of manifolds Cameron, Richard Bruce The purpose of this paper is to present a survey of some important results in the classification of differentiable manifolds. We begin with the Poincaré conjecture and its partial solution using the h-cobordism theorem. We review next the work of Kervaire and Milnor, concerned with the diffeomorphism classes of homotopy spheres. The surgery problem developed from their work, and we present its solution in the simply-connected case, by Browder. This solution amounts to the surgery invariant theorem, the fundamental surgery theorem and associated results. We end our discussion with the plumbing theorem, and several important classification theorems of Browder, Novikov and Wall. Science, Faculty of Mathematics, Department of Graduate 2010-03-24T19:37:08Z 2010-03-24T19:37:08Z 1980 Text Thesis/Dissertation http://hdl.handle.net/2429/22469 eng For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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English |
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description |
The purpose of this paper is to present a survey of some important results in the classification of differentiable manifolds. We begin with the Poincaré conjecture and its partial solution using the h-cobordism theorem. We review next the work of Kervaire and Milnor, concerned with the diffeomorphism classes of homotopy spheres. The surgery problem developed from their work, and we present its solution in the simply-connected case, by Browder. This solution amounts to the surgery invariant theorem, the fundamental surgery theorem and associated results. We end our discussion with the plumbing theorem, and several important classification theorems of Browder, Novikov and Wall. === Science, Faculty of === Mathematics, Department of === Graduate |
author |
Cameron, Richard Bruce |
spellingShingle |
Cameron, Richard Bruce The fundamental surgery theorem and the classification of manifolds |
author_facet |
Cameron, Richard Bruce |
author_sort |
Cameron, Richard Bruce |
title |
The fundamental surgery theorem and the classification of manifolds |
title_short |
The fundamental surgery theorem and the classification of manifolds |
title_full |
The fundamental surgery theorem and the classification of manifolds |
title_fullStr |
The fundamental surgery theorem and the classification of manifolds |
title_full_unstemmed |
The fundamental surgery theorem and the classification of manifolds |
title_sort |
fundamental surgery theorem and the classification of manifolds |
publishDate |
2010 |
url |
http://hdl.handle.net/2429/22469 |
work_keys_str_mv |
AT cameronrichardbruce thefundamentalsurgerytheoremandtheclassificationofmanifolds AT cameronrichardbruce fundamentalsurgerytheoremandtheclassificationofmanifolds |
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1718592030580408320 |