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Accepted

• 15.7k

Differentials in the Adams Spectral Sequence for spheres at the prime p=2

With the aid of machine computations, you can readily determine the Adams differentials up to $t-s=30$ using the multiplicative structure, the relation between Steenrod operations in $\text{Ext}_A$ ...
• 7,281
Accepted

Persistence barcodes and spectral sequences

The answer to your question is no, nobody has used persistence to improve the algorithmic efficiency of computing differentials, although of course the relationship between persistence intervals of a ...
• 14.7k
Accepted

Sphere spectrum, Character dual and Anderson dual

The Anderson dualizing spectrum $I_\mathbf{Z}$ can be defined as follows. Consider the functor $X\mapsto \mathrm{Hom}(\pi_{-\ast} X,\mathbf{Q/Z})$ from the homotopy category of spectra to graded ...
• 5,153

cup product and Steenrod operations in Serre spectral sequence

The behavior of the Steenrod squaring operations in the Serre spectral sequence was determined by Araki and independently by Vázquez (whose article I cannot locate online). However, it's a little work ...
• 48k
Accepted

"Rotated" version of the Atiyah-Hirzebruch spectral sequence

Good question. I think the answer is yes. The unnamed spectral sequence is usually referred to as the isotropy spectral sequence. For a group $G$ acting on $X$ and an abelian group $A$ of ...
• 33.4k

To compare the total, base and fiber spaces of two fiber bundles

No. Consider the map from the fibre bundle $$B\mathbb{Z} \to BD_\infty \to B\mathbb{Z}/2$$ to $* \to * \to *$. Here $D_\infty = \mathbb{Z} \rtimes \mathbb{Z}/2$ is the infinite dihedral group. You ...
Accepted

What is the relationship between spectral sequences and obstruction theory?

This is a partial answer, but every obstruction theory (in some precise sense) provides you with a spectral sequence (in fact several). Let me clarify what do I mean with obstruction theory. All this ...
• 15.7k
Accepted

• 6,526

Pullback and homology

Here is a positive answer to a slightly different question. Call a map $X\to B$ "acyclic" if it induces an isomorphism in homology for every coefficient system on $B$. (If $B$ is simply connected ...
• 48.7k