{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/99328"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/99328","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The v₁-periodic part of the Adams spectral sequence at an odd prime/","abstract":"We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the \"dancers to a discordant system.\" We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated algebraic Novikov spectral sequence converging to the 1-line of the BP chromatic spectral sequence. This result is also viewed as the calculation of a direct limit of localized modified Adams spectral sequences converging to the homotopy of the v1 -periodic sphere spectrum. As a consequence of this work, we obtain a thorough understanding of a collection of q₀-towers on the Adams E₂-page and we obtain information about the differentials between these towers. Moreover, above a line of slope 1/(p²-p-1) we can completely describe the E₂ and E₃ -pages of the mod p Adams spectral sequence, which accounts for almost all the spectral sequence in this range.","abstract_html":"We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated algebraic Novikov spectral sequence converging to the 1-line of the BP chromatic spectral sequence. This result is also viewed as the calculation of a direct limit of localized modified Adams spectral sequences converging to the homotopy of the v1 -periodic sphere spectrum. As a consequence of this work, we obtain a thorough understanding of a collection of q₀-towers on the Adams E₂-page and we obtain information about the differentials between these towers. Moreover, above a line of slope 1/(p²-p-1) we can completely describe the E₂ and E₃ -pages of the mod p Adams spectral sequence, which accounts for almost all the spectral sequence in this range.","abstract_has_math":false,"creators":["Andrews, Michael Joseph, Ph. D. Massachusetts Institute of Technology"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics.","school":null,"contributors":[],"advisors":["Haynes Miller."],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-22T22:20:52Z","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. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/99328","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Haynes Miller."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/99328"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.","In title on title-page, \"v\" is italicized, and \"1\" is subscript. Cataloged from PDF version of thesis.","Includes bibliographical references (pages 139-140)."]},{"key":"dc:description.abstract","label":"Abstract","values":["We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the \"dancers to a discordant system.\" We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated algebraic Novikov spectral sequence converging to the 1-line of the BP chromatic spectral sequence. This result is also viewed as the calculation of a direct limit of localized modified Adams spectral sequences converging to the homotopy of the v1 -periodic sphere spectrum. As a consequence of this work, we obtain a thorough understanding of a collection of q₀-towers on the Adams E₂-page and we obtain information about the differentials between these towers. Moreover, above a line of slope 1/(p²-p-1) we can completely describe the E₂ and E₃ -pages of the mod p Adams spectral sequence, which accounts for almost all the spectral sequence in this range."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["The v₁-periodic part of the Adams spectral sequence at an odd prime/"]}]}],"canonical_facts":{"dc:contributor.advisor":["Haynes Miller."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Mathematics."],"dc:creator":["Andrews, Michael Joseph, Ph. D. Massachusetts Institute of Technology"],"dc:date.accessioned":["2015-10-14T15:06:04Z"],"dc:date.available":["2015-10-14T15:06:04Z"],"dc:date.issued":["2015"],"dc:description":["Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.","In title on title-page, \"v\" is italicized, and \"1\" is subscript. Cataloged from PDF version of thesis.","Includes bibliographical references (pages 139-140)."],"dc:description.abstract":["We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the \"dancers to a discordant system.\" We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated algebraic Novikov spectral sequence converging to the 1-line of the BP chromatic spectral sequence. This result is also viewed as the calculation of a direct limit of localized modified Adams spectral sequences converging to the homotopy of the v1 -periodic sphere spectrum. As a consequence of this work, we obtain a thorough understanding of a collection of q₀-towers on the Adams E₂-page and we obtain information about the differentials between these towers. Moreover, above a line of slope 1/(p²-p-1) we can completely describe the E₂ and E₃ -pages of the mod p Adams spectral sequence, which accounts for almost all the spectral sequence in this range."],"dc:description.degree":["Ph. D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/99328"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc: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. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["The v₁-periodic part of the Adams spectral sequence at an odd prime/"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:20:52Z"}