On the Cooperations Algebra for the Second Brown-Peterson Spectrum at the Prime 2

Doctoral Dissertation

Abstract

In this thesis, we calculate the cooperations algebra for the second truncated Brown-Peterson spectrum at the prime 2. We accomplish this through the Adams spectral sequence. We begin by introducing a filtration and a splitting of the mod 2 homology for the second Brown-Peterson spectrum. From this splitting we derive a splitting on the second page of the Adams spectral sequence. This is a splitting into torsion concentrated in Adams filtration 0 and a torsion free component. We then show that this algebraic splitting lifts the stable homotopy category.

After establishing our general structural results, we turn to developing an inductive procedure for determining a basis for the Ext groups after inverting the element detecting 2. From this we determine a basis for the second page of the Adams spectral sequence modulo torsion.

Attributes

Attribute NameValues
Alternate Title
  • On the Cooperations Algebra for the Second Truncated Brown-Peterson at the Prime 2

Author Dominic Leon Culver
Contributor Mark Behrens, Research Director
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2017-05-10

Submission Date 2017-06-19
Subject
  • Mathematics

Language
  • English

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