English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Associated to any finite flag complex L there is a right-angled Coxeter groupW_L and a cubical complex \Sigma_L on which W_L acts properly and cocompactly.Its two most salient features are that (1) the link of each vertex of \Sigma_Lis L and (2) \Sigma_L is contractible. It follows that if L is a triangulationof S^{n-1}, then \Sigma_L is a contractible n-manifold. We describe a programfor proving the Singer Conjecture (on the vanishing of the reduced L^2-homologyexcept in the middle dimension) in the case of \Sigma_L where L is atriangulation of S^{n-1}. The program succeeds when n < 5. This implies theCharney-Davis Conjecture on flag triangulations of S^3. It also implies thefollowing special case of the Hopf-Chern Conjecture: every closed 4-manifoldwith a nonpositively curved, piecewise Euclidean, cubical structure hasnonnegative Euler characteristic. Our methods suggest the followinggeneralization of the Singer Conjecture.  Conjecture: If a discrete group G acts properly on a contractible n-manifold,then its L^2-Betti numbers b_i^{(2)} (G)$ vanish for i>n/2.

Vanishing theorems and conjectures for theℓ2–homology of right-angled Coxeter groups

Vanishing theorems and conjectures for theℓ²–homology of right-angled Coxeter groups