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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

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