Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/11990
Title: | The Inertia Group of Smooth 7-manifolds |
Authors: | Gollinger, William |
Advisor: | Hambleton, Ian |
Department: | Mathematics and Statistics |
Keywords: | geometric topology;inertia group;manifolds;Geometry and Topology;Geometry and Topology |
Publication Date: | Apr-2012 |
Abstract: | <p>Let $\Theta_n$ be the group of $h$-cobordism classes of homotopy spheres, i.e. closed smooth manifolds which are homotopy equivalent to $S^n$, under connected sum. A homotopy sphere $\Sigma^n$ which is not diffeomorphic to $S^n$ is called ``exotic.'' For an oriented smooth manifold $M^n$, the {\bf inertia group} $I(M)\subset\Theta_n$ is defined as the subgroup of homotopy spheres such that $M\#\Sigma$ is orientation-preserving diffeomorphic to $M$. This thesis collects together a number of results on $I(M)$ and provides a summary of some fundamental results in Geometric Topology. The focus is on dimension $7$, since it is the smallest known dimension with exotic spheres. The thesis also provides two new results: one specifically about $7$-manifolds with certain $S^1$ actions, and the other about the effect of surgery on the homotopy inertia group $I_h(M)$.</p> |
URI: | http://hdl.handle.net/11375/11990 |
Identifier: | opendissertations/6913 7946 2783742 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
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fulltext.pdf | 595.5 kB | Adobe PDF | View/Open |
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