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

Date

2019-06-15

Author

Kosta, Neza Mramor
Pamuk, Mehmetcik
Varli, Hanife

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

285
views

0
downloads

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.

Subject Keywords

Perfect discrete Morse function, Discrete vector field, Connected sum

URI

https://hdl.handle.net/11511/48889

Journal

TOPOLOGY AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/j.topol.2019.04.005

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

PERFECT DISCRETE MORSE FUNCTIONS ON CONNECTED SUMS 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, ...
Average Vector Field Splitting Method for Nonlinear Schrodinger Equation Akkoyunlu, Canan; Karasözen, Bülent (2012-05-02) The energy preserving average vector field integrator is applied to one and two dimensional Schrodinger equations with symmetric split-step method. The numerical results confirm the long-term preservation of the Hamiltonians, which is essential in simulating periodic waves.

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: https://hdl.handle.net/11511/48889.