Perfect Discrete Morse Functions On Connected Sums

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.
Applied Topology in Bedlewo 2017 (25 June - 01 July 2017 )


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.
Decomposing perfect discrete Morse functions on connected sum of 3-manifolds
Kosta, Neza Mramor; Pamuk, Mehmetcik; Varli, Hanife (2019-06-15)
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.
Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar (AIP Publishing, 2010-06-01)
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
Linear Algebraic Analysis of Fractional Fourier Domain Interpolation
Öktem, Sevinç Figen (2009-01-01)
n this work, we present a novel linear algebraic approach to certain signal interpolation problems involving the fractional Fourier transform. These problems arise in wave propagation, but the proposed approach to these can also be applicable to other areas. We see this interpolation problem as the problem of determining the unknown signal values from the given samples within some tolerable error We formulate the problem as a linear system of equations and use the condition number as a measure of redundant ...
Citation Formats
M. Pamuk, “Perfect Discrete Morse Functions On Connected Sums,” presented at the Applied Topology in Bedlewo 2017 (25 June - 01 July 2017 ), Bedlewo, Poland, 2017, Accessed: 00, 2021. [Online]. Available: