On free loop spaces of toric spaces

Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has exponential growth. Applications are made to the existence of infinitely many geometrically distinct periodic geodesics

Toral rank conjecture for moment-angle complexes

We consider an operation K \to L(K) on the set of simplicial complexes, which we call the "doubling operation". This combinatorial operation has been recently brought into toric topology by the work of Bahri, Bendersky, Cohen and Gitler on generalised moment-angle complexes (also known as K-powers). The crucial property of the doubling operation is that the moment-angle complex Z_K can be identified with the real moment-angle complex RZ_L(K) for the double L(K). As an application we prove the toral rank conjecture for Z_K by estimating the lower bound of the cohomology rank (with rational coefficients) of real moment-angle complexes RZ_K$. This paper extends the results of our previous work, where the doubling operation for polytopes was used to prove the toral rank conjecture for moment-angle manifolds.Comment: 4 pages, new references and credits adde

Parallel PARKing: Parkinson’s Genes Function in Common Pathway

Parkinson’s disease (PD) is associated with diverse genetic and environmental susceptibilities. Functional connections between PD genes have remained elusive. In this issue of Neuron, MacLeod et al. (2013) link three PD susceptibility genes, LRRK2, PARK16, and VSP35, to a common cellular pathway and show how these deficits contribute to dysfunction

The KO*-rings of BT^m, the Davis-Januszkiewicz Spaces and certain toric manifolds

This paper contains an explicit computation of the KO*-ring structure of an m-fold product of CP^{\infty}, the Davis-Januszkiewicz spaces and toric manifolds which have trivial Sq^2-homology.Comment: 34 page