The term CW-complex comes from “closure-finite with the weak topology”, where “closure-finite” refers to A3 and “weak topology” refers to A4. A finite complex is a CW-complex with only finitely many cells. Observe that if X is a finite complex, A4 is redundant, since W is the union of the compact sets φα((φ n α) −1W ), and these are closed since X is Hausdorff. If X has cells of dimension n but...

Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over R is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the questio...

In this paper, we consider the minimal cell structure problem forGCW complexes. A CW complex is a nice approximation of general topological spaces, which is constructed by repeating attaching higher dimensional cells to lower ones. A G-CW complex is its generalized version to spaces with a group action. The structure theorem for ordinary CW complexes is well-studied, and we can know the minimal...

Abstract: The classifying space E(Γ,F) for a family F of subgroups of a group Γ is defined up to Γ-homotopy as a Γ-CW -complex E(Γ,F) such that E(Γ,F) is contractible if H belongs to F and is empty otherwise. We investigate the question whether there is a finite-dimensional Γ-CW -model, a finite Γ-CW -model or a Γ-CW -model of finite type for E(Γ,F) focusing on the case where F is the family of...

We report the development of a continuous wave cavity ring-down spectroscopic (CW-CRDS) diagnostic for real-time, in situ measurement of velocity distribution functions of ions and neutral atoms in plasma. This apparatus is less complex than conventional CW-CRDS systems. We provide a detailed description of the CW-CRDS apparatus as well as measurements of argon ions and neutrals in a high-densi...

We prove that if M is a CW-complex, then the homotopy type of the skeletal filtration of M does not depend on the cell decomposition of M up to wedge products with n-disks D, when the later are given their natural CW-decomposition with unique cells of order 0, (n − 1) and n; a result resembling J.H.C. Whitehead’s work on simple homotopy types. From the Colimit Theorem for the Fundamental Crosse...

We show that a rank two finite group G admits a finite G-CW-complex X ' S with rank one prime power isotropy if and only if G does not p′-involve Qd(p) for any odd prime p. This follows from a more general theorem which allows us to construct a finite G-CW-complex by gluing together a given G-invariant family of representations defined on the Sylow subgroups of G.