Moment-angle manifolds and Panov's problem

We answer a problem posed by Panov, which is to describe the relationship between the wedge summands in a homotopy decomposition of the moment-angle complex corresponding to a disjoint union of k points and the connected sum factors in a diffeomorphism decomposition of the moment-angle manifold corresponding to the simple polytope obtained by making k vertex cuts on a standard d-simplex. This establishes a bridge between two very different approaches to moment-angle manifolds.Comment: In form accepted by International Mathematics Research Notices 201

An elementary construction of Anick's fibration

Cohen, Moore, and Neisendorfer's work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author's work on the secondary suspension, predicted the existence of a p-local fibration S^2n-1 --> T --> \Omega S^2n+1 whose connecting map is degree p^r. In a long and complex monograph, Anick constructed such a fibration for p>= 5 and r>= 1. Using new methods we give a much more conceptual construction which is also valid for p=3 and r>= 1. We go on to establish several properties of the space T.Comment: 30 page

The Role of Institutional Environments on Technical Efficiency: A Comparative Stochastic Frontier Analysis of Cotton Farmers in Benin, Burkina Faso, and Mali

This paper examines the role of institutional environments on cotton farmer technical efficiency scores in Benin, Burkina Faso, and Mali using a stochastic frontier production approach. First, the key institutional changes that have occurred with the recent market-oriented reforms are discussed. Then, farm efficiency per country is measured using cross-sectional data collected by the Cotton Sector Reform Project of the Africa, Power, and Politics Programme in 2009. Results from a one-stage estimation procedure suggest that while no technical inefficiency exists in Benin, an average technical efficiency of 69% and 46% is found in Burkina Faso and Mali, respectively. Agricultural development policies focusing on reducing the inefficiency at the farm level in Mali and Burkina Faso should be adopted; whereas policies designed to shift outward the production frontier seem more appropriate in Benin. Interestingly, institutional environment factors explaining variations in efficiency scores differ across countries. In Mali, farms that are food secure and that cultivate more hectares of cereals are more technically efficient in producing cotton. In contrast, Burkinabe farmers who are dissatisfied with the management of their producer organizations are more technically efficient. To be successful, efforts to promote efficiency would have to work in concert with the local realities in each country.Cotton, Technical Efficiency, Institutional Changes, Reforms, Benin, Burkina Faso, Mali, Agricultural and Food Policy, Consumer/Household Economics, Crop Production/Industries, Institutional and Behavioral Economics, International Development, Production Economics,

The homotopy theory of polyhedral products associated with flag complexes

If $K$ is a simplicial complex on $m$ vertices the flagification of $K$ is the minimal flag complex $K^f$ on the same vertex set that contains $K$. Letting $L$ be the set of vertices, there is a sequence of simplicial inclusions $L\to K\to K^f$. This induces a sequence of maps of polyhedral products $(\underline X,\underline A)^L\stackrel g\longrightarrow(\underline X,\underline A)^K\stackrel f\longrightarrow (\underline X,\underline A)^{K^f}$. We show that $\Omega f$ and $\Omega f\circ\Omega g$ have right homotopy inverses and draw consequences. For a flag complex $K$ the polyhedral product of the form $(\underline{CY},\underline Y)^K$ is a co-$H$-space if and only if the $1$-skeleton of $K$ is a chordal graph, and we deduce that the maps $f$ and $f\circ g$ have right homotopy inverses in this case.Comment: 25 page

Odd-primary homotopy exponents of compact simple Lie groups

We note that a recent result of the second author yields upper bounds for odd-primary homotopy exponents of compact simple Lie groups which are often quite close to the lower bounds obtained from v_1-periodic homotopy theory.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

The mod-pp homology of the classifying spaces of certain gauge groups

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_{1},\ldots,n_{\ell}\}$, where $n_{1}<\cdots <n_{\ell}$. Let $\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism class is determined by the the second Chern class having value $k\in\mathbb{Z}$. We calculate the mod-$p$ homology of the classifying space $B\mathcal{G}_k$ provided that $n_{\ell}<p-1$ and $p$ does not divide $k$.Comment: 12 page

The homotopy type of the complement of a coordinate subspace arrangement

The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy equivalent to a wedge of spheres is described. One consequence is an application in commutative algebra: certain local rings are proved to be Golod, that is, all Massey products in their homology vanish.Comment: 42 page

The homotopy type of the polyhedral product for shifted complexes

We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices,X1,...,Xn are pointed connected CW-complexes and CXi is the cone on Xi, then the polyhedral product determined by K and the pairs (C Xi , Xi ) is homotopy equivalent to a wedge of suspensions of smashes of the Xi ’s. Earlier work of the authors dealt with the special case where each Xi is a loop space. New techniques are introduced to prove the general case. These have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes. We discuss connections between polyhedral products and toric topology, combinatorics, and classical homotopy theory