The homotopy groups of the spectrum Tmf

2012/12/15 by Johan Konter, Konter, Johan · 1 citation
Mathematics · #55N34 #55P60 #55T15 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1212.3656

openalex publication_date 2012/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the structure of the homotopy groups of the connective spectrum tmf of topological modular forms and the elliptic and Adams-Novikov spectral sequences to compute the homotopy groups of the non-connective version, Tmf, of that spectrum. This is done separately for the localizations at 2, 3 and higher primes.

Citations

• The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres
• Notes on Grothendieck topologies, fibered categories and descent theory

Cited by

• On periodic families in the stable stems of height two

Related

• The \mathbb C-motivic Adams-Novikov spectral sequence for topological modular forms
• Connective versions of TMF(3)
• The descent spectral sequence for topological modular forms
• The Adams spectral sequence for 3-local tmf
• The homology of tmf