{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/33091"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/33091","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Orbispaces","abstract":"In this thesis, I introduce a new definition for orbispaces based a notion of stratified fibration and prove it's equivalence with other existing definitions. I study the notion of orbispace structures on a given stratified space. I then set up two parallel theories of stratified fibrations, one for topological spaces, and one for simplicial sets. Modulo a technical comparison between the two theories, I construct a classifying space for orbispace structures. Using a conjectural obstruction theory, I then prove that every compact orbispace is equivalent to the quotient of a compact space by the action of a compact Lie group.","abstract_html":"In this thesis, I introduce a new definition for orbispaces based a notion of stratified fibration and prove it's equivalence with other existing definitions. I study the notion of orbispace structures on a given stratified space. I then set up two parallel theories of stratified fibrations, one for topological spaces, and one for simplicial sets. Modulo a technical comparison between the two theories, I construct a classifying space for orbispace structures. Using a conjectural obstruction theory, I then prove that every compact orbispace is equivalent to the quotient of a compact space by the action of a compact Lie group.","abstract_has_math":false,"creators":["Henriques, André Gil"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Michael J. Hopkins."],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005","date_published":"2005","updated_at":"2026-07-22T22:21:24Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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