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Please use this identifier to cite or link to this item: http://hdl.handle.net/11375/11990
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dc.contributor.advisorHambleton, Ianen_US
dc.contributor.authorGollinger, Williamen_US
dc.date.accessioned2014-06-18T16:57:52Z-
dc.date.available2014-06-18T16:57:52Z-
dc.date.created2012-04-19en_US
dc.date.issued2012-04en_US
dc.identifier.otheropendissertations/6913en_US
dc.identifier.other7946en_US
dc.identifier.other2783742en_US
dc.identifier.urihttp://hdl.handle.net/11375/11990-
dc.description.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>en_US
dc.subjectgeometric topologyen_US
dc.subjectinertia groupen_US
dc.subjectmanifoldsen_US
dc.subjectGeometry and Topologyen_US
dc.subjectGeometry and Topologyen_US
dc.titleThe Inertia Group of Smooth 7-manifoldsen_US
dc.typethesisen_US
dc.contributor.departmentMathematics and Statisticsen_US
dc.description.degreeMaster of Science (MSc)en_US
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