Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Faraco, Gianluca"'
Autor:
Faraco, Gianluca, Gupta, Subhojoy
We show that the Simple Loop Conjecture holds for any representation $\rho\colon\pi_1(S)\longrightarrow \text{PSL}(2,\,\mathbb R)$ that is discrete but not faithful. That is, we show the existence of a simple closed curve in the kernel of such a repr
Externí odkaz:
http://arxiv.org/abs/2307.12066
On a Riemann surface, periods of a meromorphic differential along closed loops define a period character from the absolute homology group into the additive group of complex numbers. Fixing the period character in strata of meromorphic differentials d
Externí odkaz:
http://arxiv.org/abs/2305.06761
Autor:
Faraco, Gianluca
For every $g\ge 2$ and $n\ge4$, we provide an $n-$manifold $M$ and a continuous $2-$sided map $f\colon S\longrightarrow M$, where $S$ is a closed genus $g$ surface, such that no simple loop is contained in $\text{ker}(\,f_*\,)$. This provides a count
Externí odkaz:
http://arxiv.org/abs/2304.11946
Autor:
Faraco, Gianluca
A tessellation or tiling is a collection of sets, called tiles, that cover a plane without gaps and overlaps. The present note is an invitation to get to know the beauty and majesty of tessellations and triangulation of orientable surfaces.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/2303.17263
Autor:
Chen, Dawei, Faraco, Gianluca
We provide a complete description of realizable period representations for meromorphic differentials on Riemann surfaces with prescribed orders of zeros and poles, hyperelliptic structure, and spin parity.
Comment: 84 pages, 51 figures, 5 tables
Comment: 84 pages, 51 figures, 5 tables
Externí odkaz:
http://arxiv.org/abs/2212.05754
Publikováno v:
Dynamical Systems (2023), 1-16
Any affine map on the (n+1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. We explore the dynamical aspects of these maps by investigating about t
Externí odkaz:
http://arxiv.org/abs/2209.05236
Autor:
Faraco, Gianluca
We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving the maxima
Externí odkaz:
http://arxiv.org/abs/2207.12861
Autor:
Faraco, Gianluca, Gupta, Subhojoy
Let $S$ be a punctured surface of finite type and negative Euler characteristic. We determine all possible representations $\rho:\pi_1(S) \to \text{PSL}_2(\mathbb{C})$ that arise as the monodromy of the Schwarzian equation on $S$ with regular singula
Externí odkaz:
http://arxiv.org/abs/2109.04044
Autor:
Bouilly, Yohann, Faraco, Gianluca
Let $S$ be a closed surface of genus $g$ greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the $\Bbb T^n$-character variety giving necessary and sufficient conditions for Mod$(S)$-orbits t
Externí odkaz:
http://arxiv.org/abs/2103.14875
Let $S$ be an oriented surface of genus $g$ and $n$ punctures. The periods of any meromorphic differential on $S$, with respect to a choice of complex structure, determine a representation $\chi:\Gamma_{g,n} \to\mathbb C$ where $\Gamma_{g,n}$ is the
Externí odkaz:
http://arxiv.org/abs/2103.01580