Abstract/Details

Computational methods for higher real K-theory with applications to tmf

Hill, Michael Anthony.   Massachusetts Institute of Technology ProQuest Dissertations & Theses,  2006. 0809057.

Abstract (summary)

We begin by present a new Hopf algebra which can be used to compute the tmf homology of a space or spectrum at the prime 3. Generalizing work of Mahowald and Davis, we use this Hopf algebra to compute the tmf homology of the classifying space of the symmetric group on three elements. We also discuss the Σ3 Tate spectrum of tmf at the prime 3.

We then build on work of Hopkins and his collaborators, first computing the Adams-Novikov zero line of the homotopy of the spectrum eo4 at 5 and then generalizing the Hopf algebra for tmf to a family of Hopf algebras, one for each spectrum eop -1 at p. Using these, and using a K( p - 1)-local version, we further generalize the Davis-Mahowald result, computing the eop-1 homology of the cofiber of the transfer map BΣp S0.

We conclude by computing the initial computations needed to understand the homotopy groups of the Hopkins-Miller real K-theory spectra for heights large than p - 1 at p. The basic computations are supplemented with conjectures as to the collapse of the spectral sequences used herein to compute the homotopy. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Hopf algebra; Infinite loop space; K-theory; Tate spectrum; tmf homology
Title
Computational methods for higher real K-theory with applications to tmf
Author
Hill, Michael Anthony
Number of pages
0
Degree date
2006
School code
0753
Source
DAI-B 67/06, Dissertation Abstracts International
Advisor
Hopkins, Michael J.
University/institution
Massachusetts Institute of Technology
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
0809057
ProQuest document ID
304950986
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304950986