Complete analytic functions and Riemann Surfaces

Bennun, Hayati


Perfect Discrete Morse Functions On Connected Sums
Pamuk, Mehmetcik (2017-07-01)
In this talk, we study perfect discrete Morse functions on closed oriented n-dimensional manifolds. First, we show how to compose such functions on connected sums of manifolds. Then we discuss how to decompose such functions, particularly in dimensions 2 and 3.
Varli, Hanife; Pamuk, Mehmetcik; Kosta, Neza Mramor (2018-01-01)
We study perfect discrete Morse functions on closed, connected, oriented n-dimensional manifolds. We show how to compose such functions on connected sums of manifolds of arbitrary dimensions and how to decompose them on connected sums of closed oriented surfaces.
Perfect discrete morse functions on connected sums
Varlı, Hanife; Pamuk, Mehmetcik; Kosta, Neza Mramor; Department of Mathematics (2017)
Let $K$ be a finite, regular cell complex and $f$ be a real valued function on $K$. Then $f$ is called a textit{discrete Morse function} if for all $p$-cell $sigma in K$, the following conditions hold: begin{align*} displaystyle n_{1}=# {tau > sigma mid f(tau)leq f(sigma)} leq 1, \ n_{2}=# {nu < sigma mid f(nu)geq f(sigma)}leq 1. end{align*} A $p$-cell $sigma$ is called a textit{critical $p$-cell} if $n_{1}=n_{2}=0$. A discrete Morse function $f$ is called a textit{perfect discrete Morse function} if the nu...
Real-analytic diffeomorphisms of the circle and mapping class groups
Yüce, İlker Savaş; Korkmaz, Mustafa; Department of Mathematics (2000)
Invariant subspaces of positive operators on riesz spaces and observations on cd0(K)-spaces
Çağlar, Mert; Ercan, Zafer; Department of Mathematics (2005)
The present work consists of two main parts. In the first part, invariant subspaces of positive operators or operator families on locally convex solid Riesz spaces are examined. The concept of a weakly-quasinilpotent operator on a locally convex solid Riesz space has been introduced and several results that are known for a single operator on Banach lattices have been generalized to families of positive or close-to-them operators on these spaces. In the second part, the so-called generalized Alexandroff dupl...
Citation Formats
H. Bennun, “Complete analytic functions and Riemann Surfaces,” Middle East Technical University, 2001.