منابع مشابه
Morse Functions Statistics
We answer a question of V.I. Arnold concerning the growth rate of the number of Morse functions on the two sphere.
متن کاملConstructing discrete Morse functions
Morse theory has been considered a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse ...
متن کاملOn Optimizing Discrete Morse Functions
In 1998, Forman introduced discrete Morse theory as a tool for studying CW complexes by producing smaller, simpler-to-understand complexes of critical cells with the same homotopy types as the original complexes. This paper addresses two questions: (1) under what conditions may several gradient paths in a discrete Morse function simultaneously be reversed to cancel several pairs of critical cel...
متن کاملComputing Optimal Discrete Morse Functions
The essential structural information of discrete Morse functions is captured by so-called Morse matchings. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present first polyhedral results for the corresponding polytope and report on some preliminary computational results.
متن کاملMorse Inequalities and Zeta Functions
Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...
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ژورنال
عنوان ژورنال: Functional Analysis and Other Mathematics
سال: 2007
ISSN: 1991-0061,1863-7914
DOI: 10.1007/s11853-007-0006-8