Noncommutative ring spectra

Let A be an Ax ring spectrum. We give an explicit construction of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. Using this construction we can then study how THH(A) varies over the moduli space of AO structures on A, a problem which seems largely intractable using strictly associative replacements of A. We study how topological Hochschild cohomology of any 2-periodic Morava K-theory varies over the moduli space of AO structures and show that in the generic case, when a certain matrix describing the multiplication is invertible, the result is the corresponding Morava E-theory. If this matrix is not invertible, the result is some extension of Morava E-theory, and exactly which extension we get depends on the AO structure. To make sense of our constructions, we first set up a general framework for enriching a subcategory of the category of noncommutative sets over a category C using products of the objects of a non-E operad P in C. By viewing the simplicial category as a subcategory of the category of noncommutative sets in two different ways, we obtain two generalizations of simplicial objects.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Angeltveit, Vigleik

Advisor dc:contributor.advisor

• Haynes R. Miller.

• Mathematics.

Statement 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34549

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34549