Deformations of homotopy theories via algebraic theories
Balderrama, William
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https://hdl.handle.net/2142/110493
Description
Title
Deformations of homotopy theories via algebraic theories
Author(s)
Balderrama, William
Issue Date
2021-04-20
Director of Research (if dissertation) or Advisor (if thesis)
Rezk, Charles
Doctoral Committee Chair(s)
Stojanoska, Vesna
Committee Member(s)
Ando, Matthew
Heller, Jeremiah
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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