Domains in infinite jet spaces: -spectral sequences

Spectral Elements on Infinite Domains

Classifying Spaces and Spectral Sequences

Remark 1.3. One can see that if BG exists, it is unique up to weak equivalence by the Yoneda lemma and the fact that every space is weakly equivalent to a CW complex. We will construct two different models of BG, the classical one from Milnor, and one from Segal. The latter will have the advantage that B(G× G′) ∼= BG× BG′ Proposition 1.4. If EG is a weakly contractible space with a free action ...

Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces

In this article, we exhibit a large class of Banach spaces whose open unit balls are bounded symmetric homogeneous domains. These Banach spaces, which we call J*-algebras, are linear spaces of operators mapping one Hilbert space into another and have a kind of Jordan tripte product structure. In particular, all Hilbert spaces and all B*--algebras are J*-algebras. Moreover, all four types of the...

A spectral order for infinite-dimensional quantum spaces

In this paper we extend the spectral order of Coecke and Martin to infinite dimensional quantum states. Many properties present in the finite dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analyzed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and tha...

Jet Spaces and Arc Spaces

Before getting into details, I would like to recall the p-adic inspiration for this theory. Here is a list of things we looked at in Chapter III. (1) Polynomials f ∈ Z[X1, . . . , Xn] and their solutions over Z/pZ ' Zp/pZp, where p is a fixed prime and m ≥ 0. Such a solution can be written as x1 = a10 + a11p+ . . .+ a1mp m , . . . , xn = an0 + an1p+ . . .+ anmp m with ai ∈ {0, . . . , p− 1}. (2...