Mod Two Homology of Q≥0S 0 as an E∞ Space

Abstract

In this thesis, we consider the mod 2 homology of Q≥0S0 as an E∞ space and show the following. The homologies H*Q≥0S0 and H*C∞S0 are isomorphic as free commutative /2-algebras. The homology H*Q≥0S0 is generated as an algebra with Dyer-Lashof operations by the elements [1] and Qk[1] * [-2] with k ≥ 1, where [1] ∈ H*S0 ⊂ H*Q≥0S0 is the homology class representing 1 ∈ S0 = {0; 1}. Moreover, the homology H*C∞ P∞ maps onto H*Q0S0 as an algebra with Dyer-Lashof operations, with a nontrivial kernel in dimension 4.