sagemathgh-36310: Mod 2 (co)homology as a module over the Steenrod al…

…gebra

    
Mod 2 (co)homology as a module over the Steenrod algebra

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Implement:

- vector space duality for (co)homology of cell complexes with field
coefficients, switching between homology and cohomology
- Steenrod operations on homology and cohomology, acting from the left
and from the right

The Steenrod operation "Sq(i)" was already implemented for cohomology
rings, raising an error if it was used with a base field other than
GF(2). Now there is a new class, `CohomologyRing_mod2`, which should
only be used with that base field, and the `Sq` method is attached to
Elements of that new class.

Using Steenrod operations is more transparent: in addition to doing
`x.Sq(i)`, users can do `Sq(i) * x` or `x * Sq(i)`, or indeed `a * x` or
`x * a` for any element `a` of `SteenrodAlgebra(2)`. (The elements
`Sq(i)` generate the Steenrod algebra, but they do not constitute a full
list of the elements.)

This fixes sagemath#6103.

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URL: sagemath#36310
Reported by: John H. Palmieri
Reviewer(s): John H. Palmieri, Travis Scrimshaw

src/doc/en/reference/references/index.rst

@@ -1002,6 +1002,11 @@ REFERENCES:
             group actions}, (preprint March 2003, available on
             Mitter's MIT website).
 
+.. [Boa1982] J. M. Boardman, "The eightfold way to BP-operations",
+             in *Current trends in algebraic topology*, pp. 187–226,
+             Canadian Mathematical Society Proceedings, 2, Part 1.
+             Providence 1982. ISBN 978-0-8218-6003-8.
+
 .. [Bond2007] P. Bonderson, Nonabelian anyons and interferometry,
               Dissertation (2007). https://thesis.library.caltech.edu/2447/