All Questions
8
questions
4
votes
1
answer
172
views
$BP$-Adams Novikov Spectral Sequence or Homotopy groups of $S/3$
What is know about the homotopy groups of $S/3$ where $S/3 = \mathrm{hocofib}(S \xrightarrow{\cdot 3} S)$? Otherwise, is there some reference I can consult for the $BP$-ANSS for $S/3$?
- 151
5
votes
0
answers
218
views
Is there a systematic way to "bound" the $d_n$'s of ASS's by "pairing" them with elements in the $n$-line of the $E_2$ of the ASS of the sphere?
All details in the question are for the case $p=2$ though I expect the answer shouldn't be that different for odd primes.
Adams showed (i think it was him) the following statement:
The element $...
- 7,689
10
votes
2
answers
2k
views
Sphere spectrum, Character dual and Anderson dual
The homotopy groups of the sphere spectrum are the stable homotopy groups of spheres.
However, could you help me to appreciate the mathematical meanings of the following:
What is the significance of ...
- 10.4k
31
votes
1
answer
2k
views
K(r)-localization and monochromatic layers in the chromatic spectral sequence
While preparing some lecture notes, I had a basic point of confusion come up that I haven't been able to settle.
The $BP$-Adams spectral sequence (or $p$-local Adams-Novikov spectral sequence) for ...
- 6,258
12
votes
2
answers
1k
views
Differentials in the Adams Spectral Sequence for spheres at the prime p=2
How does one compute the differentials in the Adams Spectral Sequence for spheres at the prime 2 in the range $13\le t-s\le 20$? There seem to be 6 nonzero differentials, and at this point I only ...
- 1,147
12
votes
1
answer
942
views
What is the first interesting matric Toda bracket in the stable homotopy of the sphere?
Feel free to gloss ‘interesting’ as you see fit. One way:
1. What is the lowest degree matric Toda bracket in $\pi_\ast(S)$ that doesn't contain zero?
By ‘degree’ I mean total homotopical degree, ...
- 3,083
19
votes
2
answers
818
views
Is the 4-line of the E_2 term of the classical Adams spectral sequence known?
In other words:
What is $\mathrm{Ext}_{\mathcal{A}}^{4,t}(\mathbb{Z}/2,\mathbb{Z}/2)$?
If the 4-line is not known, how much is known about it?
Here, $\mathcal{A}$ is the 2-primary Steenrod ...
- 3,083
6
votes
1
answer
879
views
Serre spectral sequence with spectra
A friend recently asked me if i had heard anything about a stable Serre Spectral Sequence or one constructed with spectra, has any one else ever heard of this? is there any reason other than ...
- 3,696