Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Shalen, Peter"'
We prove that if $G_\phi=\langle F, t| t x t^{-1} =\phi(x), x\in F\rangle$ is the mapping torus group of an injective endomorphism $\phi: F\to F$ of a free group $F$ (of possibly infinite rank), then every two-generator subgroup $H$ of $G_\phi$ is ei
Externí odkaz:
http://arxiv.org/abs/2405.08985
Autor:
DeBlois, Jason, Shalen, Peter B.
Let $N$ be a compact, orientable hyperbolic 3-manifold whose boundary is a connected totally geodesic surface of genus $2$. If $N$ has Heegaard genus at least $5$, then its volume is greater than $2V_{\rm oct}$, where $V_{\rm oct}=3.66\ldots$ denotes
Externí odkaz:
http://arxiv.org/abs/2403.06058
Autor:
Shalen, Peter B.
Let $p$ be a point of an orientable hyperbolic $3$-manifold $M$, and let $m\ge1$ and $k\ge2$ be integers. Suppose that $\alpha_1,\ldots,\alpha_m$ are loops based at $p$ having length less than $\log(2k-1)$. We show that if $G$ denotes the subgroup of
Externí odkaz:
http://arxiv.org/abs/2301.05111
Autor:
Guzman, Rosemary K., Shalen, Peter B.
Under mild topological restrictions, we obtain new linear upper bounds for the dimension of the mod $p$ homology (for any prime $p$) of a finite-volume orientable hyperbolic $3$ manifold $M$ in terms of its volume. A surprising feature of the argumen
Externí odkaz:
http://arxiv.org/abs/2207.00040
Autor:
Guzman, Rosemary K., Shalen, Peter B.
We show that for every finite-volume hyperbolic $3$-manifold $M$ and every prime $p$ we have $\text{dim}\ H_1(M;\mathbf{F}_p)< 168.602\cdot\text{vol}\ M$. There are slightly stronger estimates if $p = 2$ or if $M$ is non-compact. This improves on a r
Externí odkaz:
http://arxiv.org/abs/2110.14847
Autor:
Guzman, Rosemary K., Shalen, Peter B.
We show that if $M$ is any closed, orientable hyperbolic $3$-manifold with ${\rm vol}\ M\le3.69$, we have ${\rm dim}\ H_1(M;{\bf F}_2)\le7$. This may be regarded as a qualitative improvement of a result due to Culler and Shalen, because the constant
Externí odkaz:
http://arxiv.org/abs/2010.03676
Autor:
Shalen, Peter B.
Let ${\mathfrak M}$ be a closed, orientable, hyperbolic 3-orbifold such that $\pi_1({\mathfrak M})$ contains no hyperbolic triangle group. We show that strict upper bounds of 0.07625, 0.1525 and 0.22875 for ${\rm vol}\ {\mathfrak M}$ imply respective
Externí odkaz:
http://arxiv.org/abs/1904.11850
Autor:
Guzman, Rosemary K., Shalen, Peter B.
We investigate the geometry of closed, orientable, hyperbolic $3$-manifolds whose fundamental groups are $k$-free for a given integer $k\ge 3$. We show that any such manifold $M$ contains a point $P$ of $M$ with the following property: If $S$ is the
Externí odkaz:
http://arxiv.org/abs/1802.08350
Autor:
Shalen, Peter B.
Let ${\mathfrak M}$ be a closed, orientable, hyperbolic 3-orbifold whose singular set is a link, and such that $\pi_1({\mathfrak M})$ contains no hyperbolic triangle group. We show that if the underlying manifold $|{\mathfrak M}|$ is irreducible, and
Externí odkaz:
http://arxiv.org/abs/1709.07413
Autor:
Shalen, Peter B.
A positive integer $m$ will be called a {\it finitistic order} for an element $\gamma$ of a group $\Gamma$ if there exist a finite group $G$ and a homomorphism $h:\Gamma\to G$ such that $h(\gamma)$ has order $m$ in $G$. It is shown that up to conjuga
Externí odkaz:
http://arxiv.org/abs/1104.0410