{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/74656"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/74656","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Surgery spaces of crystallographic groups","abstract":"Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H<sub>*</sub>(R<sup>n</sup> /Γ; L(p)) → L<sub>*</sub><sup>-∞</sup>(Γ).","abstract_html":"Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H&lt;sub&gt;*&lt;/sub&gt;(R&lt;sup&gt;n&lt;/sup&gt; /Γ; L(p)) → L&lt;sub&gt;*&lt;/sub&gt;&lt;sup&gt;-∞&lt;/sup&gt;(Γ).","abstract_has_math":false,"creators":["Yamasaki, Masayuki"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. 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The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H<sub>*</sub>(R<sup>n</sup> /Γ; L(p)) → L<sub>*</sub><sup>-∞</sup>(Γ)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Surgery spaces of crystallographic groups"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Quinn, Frank"],"dc:contributor.committeemember":["Arnold, Jesse T.","McCoy, Robert A.","Olin, Robert F.","Snider, R.L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Yamasaki, Masayuki"],"dc:date.accessioned":["2017-01-30T21:23:31Z"],"dc:date.available":["2017-01-30T21:23:31Z"],"dc:date.issued":["1982"],"dc:description.abstract":["Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H<sub>*</sub>(R<sup>n</sup> /Γ; L(p)) → L<sub>*</sub><sup>-∞</sup>(Γ)."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/74656"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Surgery spaces of crystallographic groups"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. 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