arXiv subjects

Grigori Avramidi

Publications and source records attributed to Grigori Avramidi.

21 records · Page 2Linked to original sources

arXiv2013

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

We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $π_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of a compact manifold $\M$ with boundary $\partial\barM$. We show that for each $π_1$-injective boundary component $C$ of $\M$, the map $i_*$ induced by inclusion $i\colon C\rightarrow \M$ has infinite index image $i_*(π_1 C)$ in $π_1 \M$. We also prove that $M$ cannot be homotoped to be contained in $\partial\M$.

math.GT↗

arXiv2011

Periodic flats and group actions on locally symmetric spaces

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $\geq 3$, no metric $g$ has more symmetry than the locally symmetric metric. We also show that if $g$ is a finite volume metric that is not locally symmetric, then its lift to the universal cover has discrete isometry group.

math.GT↗

arXiv2011

Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves

We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and aspherical locally symmetric spaces with non-vanishing Euler characteristic. In the irreducible locally symmetric case, we show that no complete metric has more symmetry than the locally symmetric metric. In the moduli space case, we build on work of Farb and Weinberger and prove an analogue of Royden's theorem for complete finite volume metrics.

math.GT↗