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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ withsectional curvature $-1<K<0$. We prove that $\pi_1 M$ cannot be a 3-manifoldgroup. A classical theorem of Gromov says that $M$ is homeomorphic to theinterior of a compact manifold $\M$ with boundary $\partial\barM$. We show thatfor each $\pi_1$-injective boundary component $C$ of $\M$, the map $i_*$induced by inclusion $i\colon C\rightarrow \M$ has infinite index image$i_*(\pi_1 C)$ in $\pi_1 \M$. We also prove that $M$ cannot be homotoped to becontained in $\partial\M$.

Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups