{"id":{"repo_id":"whiterose","oai_identifier":"oai:etheses.whiterose.ac.uk:1103"},"canonical_url":"https://search.dev.ndltd.org/etd/whiterose/oai:etheses.whiterose.ac.uk:1103","repository":{"repo_id":"whiterose","name":"White Rose University Consortium","base_url":"https://etheses.whiterose.ac.uk/cgi/oai2"},"display":{"title":"The connective K theory of semidihedral groups","abstract":"The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8).","abstract_html":"The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8).","abstract_has_math":false,"creators":["Rodtes, Kijti"],"institution":"University of Sheffield","degree_name":"Ph.D","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Greenlees, John Patrick Campbell"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-11","date_published":"2010-11","updated_at":"2026-07-24T06:04:07Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.538013"],"render_values":[{"text":"uk.bl.ethos.538013","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Greenlees, John Patrick Campbell"]},{"key":"dc:creator","label":"Author","values":["Rodtes, Kijti"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-11"]},{"key":"dc:date.issued","label":"Date","values":["2010-11"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["University of Sheffield"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics and Statistics (Sheffield)"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Sheffield"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://etheses.whiterose.ac.uk/id/eprint/1103/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.538013"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://etheses.whiterose.ac.uk/id/eprint/1103/2/Rodtes%2C_Kijtie.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8)."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["The connective K theory of semidihedral groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Greenlees, John Patrick Campbell"],"dc:creator":["Rodtes, Kijti"],"dc:date":["2010-11"],"dc:date.issued":["2010-11"],"dc:description.abstract":["The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8)."],"dc:format":["text"],"dc:identifier":["uk.bl.ethos.538013"],"dc:identifier.uri":["https://etheses.whiterose.ac.uk/id/eprint/1103/2/Rodtes%2C_Kijtie.pdf"],"dc:publisher.commercial":["University of Sheffield"],"dc:publisher.department":["School of Mathematics and Statistics (Sheffield)"],"dc:publisher.institution":["University of Sheffield"],"dc:relation.isreferencedby":["https://etheses.whiterose.ac.uk/id/eprint/1103/"],"dc:title":["The connective K theory of semidihedral groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D"]},"updated_at":"2026-07-24T06:04:07Z"}