{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/79974"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/79974","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Detecting Mapping Spaces and Spaces with Complexity One","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Bittner, Alyson; 0000-0001-5495-5062"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Badzioch, Bernard","Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-07-30T15:11:31Z","date_published":"2019-07-30T15:11:31Z","updated_at":"2026-07-27T19:05:21Z","subjects":["mathematics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/79974","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Badzioch, Bernard","Mathematics"]},{"key":"dc:creator","label":"Author","values":["Bittner, Alyson; 0000-0001-5495-5062"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-07-30T15:11:31Z","2019","2019-05-16 09:43:10"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/79974"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","In this thesis we will prove two main results regarding a space A following from information about mapping spaces out of a space A. We show if A is a finite CW-complex such that algebraic theories detect mapping spaces out of A, then A has the homology type of a wedge of spheres of the same dimension. Furthermore, if A is simply connected then A has the homotopy type of a wedge of spheres.The A-cellular approximation of a space X is the space that contains the most information we can possibly recover from X given the mapping space from A to X. The A-complexity of a space X is an ordinal number that quantifies how difficult it is to build an A-cellular approximation of X. We show that if A is a space such that mapping spaces out of A can be described by the algebraic theory associated to A, then the A-complexity of any space X is at most 1. This holds in particular for spheres and spheres localized at a set of primes."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Detecting Mapping Spaces and Spaces with Complexity One"]}]}],"canonical_facts":{"dc:contributor":["Badzioch, Bernard","Mathematics"],"dc:creator":["Bittner, Alyson; 0000-0001-5495-5062"],"dc:date":["2019-07-30T15:11:31Z","2019","2019-05-16 09:43:10"],"dc:description":["Ph.D.","In this thesis we will prove two main results regarding a space A following from information about mapping spaces out of a space A. We show if A is a finite CW-complex such that algebraic theories detect mapping spaces out of A, then A has the homology type of a wedge of spheres of the same dimension. Furthermore, if A is simply connected then A has the homotopy type of a wedge of spheres.The A-cellular approximation of a space X is the space that contains the most information we can possibly recover from X given the mapping space from A to X. The A-complexity of a space X is an ordinal number that quantifies how difficult it is to build an A-cellular approximation of X. We show that if A is a space such that mapping spaces out of A can be described by the algebraic theory associated to A, then the A-complexity of any space X is at most 1. This holds in particular for spheres and spheres localized at a set of primes."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/79974"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["mathematics"],"dc:title":["Detecting Mapping Spaces and Spaces with Complexity One"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:21Z"}