scholarly journals Heegaard splittings and singularities of the product map of Morse functions

2013 ◽  
Vol 366 (4) ◽  
pp. 2209-2226
Author(s):  
Kazuto Takao
Keyword(s):  
Heegaard Splittings ◽  
Morse Functions ◽  
Product Map

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

Local uniqueness of certain geodesics related to Heegaard splittings

2018 ◽  
Vol 27 (09) ◽  
pp. 1842003
Author(s):  
Liang Liang ◽  
Fengling Li ◽  
Fengchun Lei ◽  
Jie Wu
Keyword(s):  
Heegaard Splitting ◽  
Sufficient Condition ◽  
Heegaard Splittings ◽  
Local Uniqueness ◽  
Uniqueness Property

Suppose [Formula: see text] is a Heegaard splitting and [Formula: see text] is an essential separating disk in [Formula: see text] such that a component of [Formula: see text] is homeomorphic to [Formula: see text], [Formula: see text]. In this paper, we prove that if there is a locally complicated simplicial path in [Formula: see text] connecting [Formula: see text] to [Formula: see text], then the geodesic connecting [Formula: see text] to [Formula: see text] is unique. Moreover, we give a sufficient condition such that [Formula: see text] is keen and the geodesic between any pair of essential disks on the opposite sides has local uniqueness property.

The amalgamation of high distance Heegaard splittings is always efficient

2008 ◽  
Vol 341 (3) ◽  
pp. 707-715 ◽  
Author(s):  
Tsuyoshi Kobayashi ◽  
Ruifeng Qiu
Keyword(s):  
Heegaard Splittings

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.

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