Decomposing perfect discrete Morse functions on connected sum of 3-manifolds

Kosta, Neza Mramor
Pamuk, Mehmetcik
Varli, Hanife
In this paper, we show that if a closed, connected, oriented 3-manifold M = M-1 # M-2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M-1 and M-2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition.


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...
Discrete bifurcation diagrams and persistence
Örnek, Türkmen; Pamuk, Semra; Department of Mathematics (2018)
Let fti : M → R be a discrete Morse function on a cell complex M for each t0 < t1 < ... < tn = 1. Let us denote slice as Mi = M ×{ti} ⊂ M × I and let Vi be the discrete vector field on each slice. After extending the discrete vector field on each slice to a discrete vector field on all of M ×I, a discrete bifurcation diagram is obtained by connecting critical cells of the slices. In”Birth and Death in Discrete MorseTheory”(King,Knudson,Mramor), a solution about finding the discrete bifurcation diagram has been ...
Generalized rotation symmetric and dihedral symmetric boolean functions - 9 variable boolean functions with nonlinearity 242
Kavut, Selcuk; Yucel, Melek Diker (2007-12-20)
Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral Symmetric Boolean Functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, ...
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
Citation Formats
N. M. Kosta, M. Pamuk, and H. Varli, “Decomposing perfect discrete Morse functions on connected sum of 3-manifolds,” TOPOLOGY AND ITS APPLICATIONS, pp. 139–147, 2019, Accessed: 00, 2020. [Online]. Available: