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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper we prove that for all $n=4k-2$, $k\ge2$ there exists closed$n$-dimensional Riemannian manifolds $M$ with negative sectional curvature thatdo not have the homotopy type of a locally symmetric space, such that$\pi_{1}(\mathcal{T}^{<0}(M))$ is non-trivial. $\mathcal{T}^{<0}(M)$ denotesthe Teichm\"uller space of all negatively curved Riemannian metrics on $M$,which is the topological quotient of the space of all negatively curved metricsmodulo the space of self-diffeomorphisms of $M$ that are homotopic to theidentity. Gromov Thurston branched cover manifolds provide examples ofnegatively curved manifolds that do not have the homotopy type of a locallysymmetric space. These manifolds will be used in this paper to prove the abovestated result.

Teichm\"uller space of negatively curved metrics on Gromov Thurston Manifolds is not contractible