{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/239413"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/239413","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Witt groups of complex varieties","abstract":"The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. Specifically, we introduce comparison maps from the Grothendieck-Witt and Witt groups of a smooth complex variety to the KO-groups of the underlying topological space and analyse their behaviour. We focus on two particularly favourable situations. Firstly, we explicitly compute the Witt groups of smooth complex curves and surfaces. Using the theory of Stiefel-Whitney classes, we obtain a satisfactory description of the comparison maps in these low-dimensional cases. Secondly, we show that the comparison maps are isomorphisms for smooth cellular varieties. This result applies in particular to projective homogeneous spaces. By extending known computations in topology, we obtain an additive description of the Witt groups of all projective homogeneous varieties that fall within the class of hermitian symmetric spaces.","abstract_html":"The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. Specifically, we introduce comparison maps from the Grothendieck-Witt and Witt groups of a smooth complex variety to the KO-groups of the underlying topological space and analyse their behaviour. We focus on two particularly favourable situations. Firstly, we explicitly compute the Witt groups of smooth complex curves and surfaces. Using the theory of Stiefel-Whitney classes, we obtain a satisfactory description of the comparison maps in these low-dimensional cases. Secondly, we show that the comparison maps are isomorphisms for smooth cellular varieties. This result applies in particular to projective homogeneous spaces. By extending known computations in topology, we obtain an additive description of the Witt groups of all projective homogeneous varieties that fall within the class of hermitian symmetric spaces.","abstract_has_math":false,"creators":["Zibrowius, Marcus"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-07-12","date_published":"2011-07-12","updated_at":"2026-07-22T22:24:10Z","subjects":["Witt groups","KO-theory"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2a2ec853-c0f8-4bec-a334-659a7e343417/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.16217","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["This work was supported by the Engineering and Physical Sciences Research Council [grant number LFAG/067] and by the Cambridge Philosophical Society."]},{"key":"dc:creator","label":"Author","values":["Zibrowius, Marcus"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2011-07-12"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["http://www.dspace.cam.ac.uk/handle/1810/239413","https://www.repository.cam.ac.uk/handle/1810/239413"]},{"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":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Witt groups","KO-theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2a2ec853-c0f8-4bec-a334-659a7e343417/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.16217"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/0fd44a2f-5920-4e59-a4b3-e7fdcf569541/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. Specifically, we introduce comparison maps from the Grothendieck-Witt and Witt groups of a smooth complex variety to the KO-groups of the underlying topological space and analyse their behaviour. We focus on two particularly favourable situations. Firstly, we explicitly compute the Witt groups of smooth complex curves and surfaces. Using the theory of Stiefel-Whitney classes, we obtain a satisfactory description of the comparison maps in these low-dimensional cases. Secondly, we show that the comparison maps are isomorphisms for smooth cellular varieties. This result applies in particular to projective homogeneous spaces. By extending known computations in topology, we obtain an additive description of the Witt groups of all projective homogeneous varieties that fall within the class of hermitian symmetric spaces."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["781e0a26851a06d2de7234b6ade7c294","48dcdf38f646da27e5e4bc6c1893d4fc"]},{"key":"dc:title","label":"Title","values":["Witt groups of complex varieties"]}]}],"canonical_facts":{"dc:contributor.sponsor":["This work was supported by the Engineering and Physical Sciences Research Council [grant number LFAG/067] and by the Cambridge Philosophical Society."],"dc:creator":["Zibrowius, Marcus"],"dc:date.issued":["2011-07-12"],"dc:description.abstract":["The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. 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By extending known computations in topology, we obtain an additive description of the Witt groups of all projective homogeneous varieties that fall within the class of hermitian symmetric spaces."],"dc:format.checksum.md5":["781e0a26851a06d2de7234b6ade7c294","48dcdf38f646da27e5e4bc6c1893d4fc"],"dc:identifier.doi":["10.17863/CAM.16217"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/0fd44a2f-5920-4e59-a4b3-e7fdcf569541/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["http://www.dspace.cam.ac.uk/handle/1810/239413","https://www.repository.cam.ac.uk/handle/1810/239413"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2a2ec853-c0f8-4bec-a334-659a7e343417/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Witt groups","KO-theory"],"dc:title":["Witt groups of complex varieties"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:10Z"}