scholarly journals On the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$

2021 ◽  
Author(s):  
Dominic Leon Culver ◽  
Paul VanKoughnett
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence

AbstractAs a step towards understanding the $$\mathrm {tmf}$$ tmf -based Adams spectral sequence, we compute the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$ tmf ∧ tmf , using a small presentation of $$L_{K(1)}\mathrm {tmf}$$ L K ( 1 ) tmf due to Hopkins. We also describe the K(1)-local $$\mathrm {tmf}$$ tmf -based Adams spectral sequence.

scholarly journals Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology

1999 ◽  
Vol 42 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Andrew Baker
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Hecke Operators ◽  
Elliptic Cohomology

AbstractHecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.

Some infinite families in the stable homotopy of spheres

1987 ◽  
Vol 101 (3) ◽  
pp. 477-485 ◽  
Author(s):  
Wen-Hsiung Lin
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Stable Homotopy Of Spheres

The classical Adams spectral sequence [1] has been an important tool in the computation of the stable homotopy groups of spheres . In this paper we make another contribution to this computation.

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