<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> / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/11990 |
| Date | 04 1900 |
| Creators | Gollinger, William |
| Contributors | Hambleton, Ian, Mathematics and Statistics |
| Source Sets | McMaster University |
| Detected Language | English |
| Type | thesis |
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