ﻻ يوجد ملخص باللغة العربية
A pair $(alpha, beta)$ of simple closed geodesics on a closed and oriented hyperbolic surface $M_g$ of genus $g$ is called a filling pair if the complementary components of $alphacupbeta$ in $M_g$ are simply connected. The length of a filling pair is defined to be the sum of their individual lengths. In cite{Aou}, Aougab-Huang conjectured that the length of any filling pair on $M$ is at least $frac{m_{g}}{2}$, where $m_{g}$ is the perimeter of the regular right-angled hyperbolic $left(8g-4right)$-gon. In this paper, we prove a generalized isoperimetric inequality for disconnected regions and we prove the Aougab-Huang conjecture as a corollary.
In our earlier paper (K. Eda, U. Karimov, and D. Repovv{s}, emph{A construction of simply connected noncontractible cell-like two-dimensional Peano continua}, Fund. Math. textbf{195} (2007), 193--203) we introduced a cone-like space $SC(Z)$. In the p
Let $F_g$ be a closed orientable surface of genus $g$. A set $Omega = { gamma_1, dots, gamma_s}$ of pairwise non-homotopic simple closed curves on $F_g$ is called a emph{filling system} or simply a emph{filling} of $F_g$, if $F_gsetminus Omega$ is a
We construct a functor $AC(-,-)$ from the category of path connected spaces $X$ with a base point $x$ to the category of simply connected spaces. The following are the main results of the paper: (i) If $X$ is a Peano continuum then $AC(X,x)$ is a cel
We outline the proof that non-triangulable manifolds exist in any dimension greater than four. The arguments involve homology cobordism invariants coming from the Pin(2) symmetry of the Seiberg-Witten equations. We also explore a related construction
The classifying space for the framed Haefliger structures of codimension $q$ and class $C^r$ is $(2q-1)$-connected, for $1le rleinfty$. The corollaries deal with the existence of foliations, with the homology and the perfectness of the diffeomorphism