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Title:Deformations of homotopy theories via algebraic theories
Author(s):Balderrama, William
Director of Research:Rezk, Charles
Doctoral Committee Chair(s):Stojanoska, Vesna
Doctoral Committee Member(s):Ando, Matthew; Heller, Jeremiah
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Homotopy theory
Abstract:We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, we give some tools for working with K(h)-local E-infinity algebras over a Lubin-Tate spectrum of height h, and use these to produce new E-infinity complex orientations at heights h <= 2.
Issue Date:2021-04-20
Type:Thesis
URI:http://hdl.handle.net/2142/110493
Rights Information:Copyright 2021 William Balderrama
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05


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