Incidence relations among the cells of a regular CW complex produce a 2category of entrance paths whose classifying space is homotopy-equivalent to that complex. We show here that each acyclic partial matching on (the cells of) such a complex corresponds precisely to a homotopy-preserving localization of the associated entrance path category. Restricting attention further to the full localized ...

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

suspensions of A and attaching cones on suspensions of A (see [5, corollary 3.7]). If A = S, then a relative S–CW–complex is essentially an ordinary relative CW– complex. Any pointed map f : X → Y can be factored as a composition (X → Y ′ p → Y ), where (Y ′, X) is a relative A–CW–complex and p induces a weak equivalence of mapping spaces p? : map?(A, Y ′)→ map?(A, Y ). Let X be a pointed space...

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S 5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

In his pioneering work from the late 1940s, J.H.C. Whitehead established the category of CW-complexes as the natural framework for much of homotopy theory. A key role in this theory is played by the cellular chain complex of the universal cover of a connected CW-complex, which in turn is tightly connected to (co-)homology with local coefficients. In [8], we revisit these classical topics, drawi...

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S 5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

We exhibit 3-generator Artin groups which have finite 2-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a 2-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be s...

Nucleotide-activated sugars are essential substrates for plant cell-wall carbohydrate-polymer biosynthesis. The most prevalent grass cell wall (CW) sugars are glucose (Glc), xylose (Xyl), and arabinose (Ara). These sugars are biosynthetically related via the UDP-sugar interconversion pathway. We sought to target and generate UDP-sugar interconversion pathway transgenic Brachypodium distachyon l...