{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/353706"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/353706","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations","abstract":"In this thesis, we study the homology of configuration spaces of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. In Chapter 2, we prove a version of the scanning isomorphism that is “untwisted” and equivariant with the mapping class group action. We further prove that scanning remembers a product arising from superposing configurations. We apply this equivariant scanning to compute the rational cohomology of unordered configurations of surfaces with boundary. In Chapter 3, we adapt certain cellular decompositions of compactified configuration spaces to obtain the kernel of the mapping class group action on the homology of unordered configurations of both kinds of surfaces and with any coeffiecients. Finally, in Chapter 4, we geometrically construct mapping classes deep in the Johnson filtration that act non-trivially on the homology of ordered configurations, in support of a conjecture by Bianchi, Miller and Wilson.","abstract_html":"In this thesis, we study the homology of configuration spaces of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. In Chapter 2, we prove a version of the scanning isomorphism that is “untwisted” and equivariant with the mapping class group action. We further prove that scanning remembers a product arising from superposing configurations. We apply this equivariant scanning to compute the rational cohomology of unordered configurations of surfaces with boundary. In Chapter 3, we adapt certain cellular decompositions of compactified configuration spaces to obtain the kernel of the mapping class group action on the homology of unordered configurations of both kinds of surfaces and with any coeffiecients. Finally, in Chapter 4, we geometrically construct mapping classes deep in the Johnson filtration that act non-trivially on the homology of ordered configurations, in support of a conjecture by Bianchi, Miller and Wilson.","abstract_has_math":false,"creators":["Stavrou, Andreas"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Randal-Williams, Oscar"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-04-03","date_published":"2023-04-03","updated_at":"2026-07-22T22:24:11Z","subjects":["configuration spaces","homology computations","mapping class groups","surfaces","topology"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/a088c675-a536-425e-9f15-f51df02f5a2e/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.99769","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Randal-Williams, Oscar"]},{"key":"dc:creator","label":"Author","values":["Stavrou, Andreas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2023-04-03"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/353706"]},{"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":["configuration spaces","homology computations","mapping class groups","surfaces","topology"]}]},{"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/a088c675-a536-425e-9f15-f51df02f5a2e/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.99769"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ea7ff569-6462-4b8a-9377-40997ed57ce8/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we study the homology of configuration spaces of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. In Chapter 2, we prove a version of the scanning isomorphism that is “untwisted” and equivariant with the mapping class group action. We further prove that scanning remembers a product arising from superposing configurations. We apply this equivariant scanning to compute the rational cohomology of unordered configurations of surfaces with boundary. In Chapter 3, we adapt certain cellular decompositions of compactified configuration spaces to obtain the kernel of the mapping class group action on the homology of unordered configurations of both kinds of surfaces and with any coeffiecients. Finally, in Chapter 4, we geometrically construct mapping classes deep in the Johnson filtration that act non-trivially on the homology of ordered configurations, in support of a conjecture by Bianchi, Miller and Wilson."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["ae29c428ebfab367561bb79908fc7bb5","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Randal-Williams, Oscar"],"dc:creator":["Stavrou, Andreas"],"dc:date.issued":["2023-04-03"],"dc:description.abstract":["In this thesis, we study the homology of configuration spaces of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. 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