We provide unipotent factorizations of vector bundle automorphisms real and complex bundles over finite dimensional locally CW-complexes. This generalizes work Thurston–Vaserstein Vaserstein for trivial bundles. also address two symplectic cases propose a geometric analog the problem in setting holomorphic Stein manifolds.

Ganea conjectured that for any finite CW complex and any k > 0, cat(X×Sk) = cat(X) + 1. In this paper we prove two special cases of this conjecture. The main result is the following. Let X be a (p − 1) connected n dimensional CW complex (not necessarily finite). We show that if cat(X) = ⌊ n p ⌋ + 1 and n 6≡ −1 mod p (which implies p > 1), then cat(X×Sk) = cat(X) + 1. This is proved by showing t...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

In [DP03], [Ra02] it was proven that the complement to a hyperplane arrangement in C is a minimal space, i.e. it has the homotopy type of a CW -complex with exactly as many i-cells as the i-th Betti number bi. The arguments use (relative) Morse theory and Lefschetz type theorems. This result of ”existence” was refined in the case of complexified real arrangements in [Yo05]. The author consider ...

A discrete Morse function for a simplicial complex describes how to construct a homotopy equivalent CW-complex with hopefully fewer cells. We associate a boolean function with the simplicial complex and construct a discrete Morse function using its Fourier transform. Methods from theoretical computer science by O’Donnell, Saks, Schramm, and Servedio, together with experimental data on complexes...

Effects of photoperiod on growth, eating patterns and clearance rate, secretion rate and half-life of growth hormone in serum were assessed in Holstein heifers. Sixty-four prepubertal heifers (avg body wt 102 kg) were blocked by weight into four groups of 16. Within block, each animal was randomly assigned to one of four photoperiod treatments: 16 h of cool-white fluorescent light:8 h dark (CW-...