Deformations of homotopy theories via algebraic theories

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Balderrama, William

Contributors dc:contributor

• Rezk, Charles
• Stojanoska, Vesna
• Ando, Matthew
• Heller, Jeremiah

• Homotopy theory

Statement dc:rights

• Copyright 2021 William Balderrama

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/110493

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/110493