454 research outputs found
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
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