Homology of the Infinite Symmetric Group

The modulo 2 cohomology algebras of symmetric groups

“…As well known, H*(C~) is a Hopf algebra over Z2 (see Nakaoka [10]). Further, every element of this algebra has a infinite degree since the usual homomorphism H*(Vm)OH*(~m)-±H*(~2m) is injective for any m. So according to the Milnor-Moore theorem, H*() is a polynomial algebra.…”

“…From the dimensional consideration, we easily obtain the main theorem of this paper. 4 (ii) By means of the Milnor-Moore theorem on structure of Hopf alge bras, Nakaoka showed in [10] that H*() is a poylnomial algebra . But he did not obtain any information on generators of the algebra except for the dimension of generators.…”

The mod 2 equivariant cohomology algebras of configuration spaces

“…As a consequence, we have the following proposition essentially due to Steenrod [20], Nakaoka [12]. [6], [12] …”

Stable homology of automorphism groups of free groups

“…The homology groups H k (Σ n ) are completely known. With finite coefficients the calculation was done by Nakaoka and can be found in [Nak61]. We will not quote the result here.…”