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Softcover ISBN:  9781470437886 
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Softcover ISBN:  9781470437886 
Product Code:  MEMO/262/1269 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470455118 
Product Code:  MEMO/262/1269.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470437886 
eBook ISBN:  9781470455118 
Product Code:  MEMO/262/1269.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 262; 2019; 159 ppMSC: Primary 14; 55; Secondary 16
The author presents a detailed analysis of 2complete stable homotopy groups, both in the classical context and in the motivic context over \(\mathbb C\). He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over \(\mathbb C\) through the 70stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59stem. He also describes the complete calculation to the 65stem, but defers the proofs in this range to forthcoming publications.
In addition to finding all Adams differentials, the author also resolves all hidden extensions by \(2\), \(\eta \), and \(\nu \) through the 59stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences.
The author also computes the motivic stable homotopy groups of the cofiber of the motivic element \(\tau \). This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of \(\tau \) are the same as the \(E_2\)page of the classical AdamsNovikov spectral sequence. This allows him to compute the classical AdamsNovikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.

Table of Contents

Chapters

1. Introduction

2. The cohomology of the motivic Steenrod algebra

3. Differentials in the Adams spectral sequence

4. Hidden extensions in the Adams spectral sequence

5. The cofiber of $\tau $

6. Reverse engineering the AdamsNovikov spectral sequence

7. Tables

8. Charts


Additional Material

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The author presents a detailed analysis of 2complete stable homotopy groups, both in the classical context and in the motivic context over \(\mathbb C\). He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over \(\mathbb C\) through the 70stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59stem. He also describes the complete calculation to the 65stem, but defers the proofs in this range to forthcoming publications.
In addition to finding all Adams differentials, the author also resolves all hidden extensions by \(2\), \(\eta \), and \(\nu \) through the 59stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences.
The author also computes the motivic stable homotopy groups of the cofiber of the motivic element \(\tau \). This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of \(\tau \) are the same as the \(E_2\)page of the classical AdamsNovikov spectral sequence. This allows him to compute the classical AdamsNovikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.

Chapters

1. Introduction

2. The cohomology of the motivic Steenrod algebra

3. Differentials in the Adams spectral sequence

4. Hidden extensions in the Adams spectral sequence

5. The cofiber of $\tau $

6. Reverse engineering the AdamsNovikov spectral sequence

7. Tables

8. Charts