{"id":{"repo_id":"wayne-thes","oai_identifier":"oai:digitalcommons.wayne.edu:oa_dissertations-1799"},"canonical_url":"https://search.dev.ndltd.org/etd/wayne-thes/oai:digitalcommons.wayne.edu:oa_dissertations-1799","repository":{"repo_id":"wayne-thes","name":"Wayne State University","base_url":"https://digitalcommons.wayne.edu/do/oai/"},"display":{"title":"Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications","abstract":"<p>We construct Power operations in the K\"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K\"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.</p>","abstract_html":"&lt;p&gt;We construct Power operations in the K&quot;unneth spectral sequence and the <span class=\"etd-inline-math\">C<sub>2</sub></span> equivariant Adams spectral sequence. While the operations in the K&quot;unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having <span class=\"etd-inline-math\">E<sub>i</sub>nfty</span> ring maps. The operations in the <span class=\"etd-inline-math\">C<sub>2</sub></span>-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.&lt;/p&gt;","abstract_has_math":true,"creators":["Tilson, Sean Michael"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Robert R. Bruner"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-02T08:00:00Z","date_published":"2013-01-02T08:00:00Z","updated_at":"2026-07-24T05:59:26Z","subjects":["Dyer-Lashof","power operations","ring spectra","spectral sequence","stable homotopy","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/800","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Robert R. Bruner"]},{"key":"dc:creator","label":"Author","values":["Tilson, Sean Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dyer-Lashof","power operations","ring spectra","spectral sequence","stable homotopy","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/800"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We construct Power operations in the K\"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K\"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.</p>"]},{"key":"dc:title","label":"Title","values":["Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications"]}]}],"canonical_facts":{"dc:contributor":["Robert R. Bruner"],"dc:creator":["Tilson, Sean Michael"],"dc:date.available":["2013-01-01T08:00:00Z"],"dc:description.abstract":["<p>We construct Power operations in the K\"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K\"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.</p>"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/800"],"dc:subject":["Dyer-Lashof","power operations","ring spectra","spectral sequence","stable homotopy","Mathematics"],"dc:title":["Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:59:26Z"}