Local moves of the Stein factorization of the product map of two functions on a 3-manifold

2021 ◽  
pp. 1-31
Author(s):  
Kazuto Takao
Keyword(s):  
Morse Functions ◽  
Product Map

We give some local moves of the Stein factorization of the product map of two Morse functions on a closed orientable smooth [Formula: see text]-manifold which can be realized by isotopies of the functions.

scholarly journals Morse functions on cobordisms

2011 ◽  
Vol 63 (1) ◽  
pp. 146-157
Author(s):  
V. V. Sharko
Keyword(s):  
Morse Functions

scholarly journals Tight complexes in 3-space admit perfect discrete Morse functions

2015 ◽  
Vol 45 ◽  
pp. 71-84 ◽  
Author(s):  
Karim Adiprasito ◽  
Bruno Benedetti
Keyword(s):  
Morse Functions

A minimal distal map on the torus with sub-exponential measure complexity

2018 ◽  
Vol 40 (4) ◽  
pp. 953-974 ◽  
Author(s):  
WEN HUANG ◽  
LEIYE XU ◽  
XIANGDONG YE
Keyword(s):  
Dynamical System ◽  
Probability Measure ◽  
Borel Probability Measure ◽  
Skew Product ◽  
Topological Dynamical System ◽  
Borel Probability ◽  
Product Map

In this paper the notion of sub-exponential measure complexity for an invariant Borel probability measure of a topological dynamical system is introduced. Then a minimal distal skew product map on the torus with sub-exponential measure complexity is constructed.

scholarly journals Counting and Discrete Morse Theory

2019 ◽  
Vol 21 (1) ◽  
Author(s):  
Andrew Sack
Keyword(s):  
Morse Theory ◽  
Vector Fields ◽  
Discrete Morse Theory ◽  
Gradient Vector ◽  
Morse Functions

We examine enumerating discrete Morse functions on graphs up to equivalence by gradient vector fields and by restrictions on the codomain.  We give formulae for the number of discrete Morse functions on specific classes of graphs (line, cycle, and bouquet of circles).

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