scholarly journals Homotopy Types of Stabilizers and Orbits of Morse Functions on Surfaces

2006 ◽  
Vol 29 (3) ◽  
pp. 241-285 ◽  
Author(s):  
Sergiy Maksymenko
Keyword(s):  
Morse Functions ◽  
Homotopy Types

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

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).

scholarly journals Extreme nonuniqueness of end-sum

2020 ◽  
pp. 1-43
Author(s):  
Jack S. Calcut ◽  
Craig R. Guilbault ◽  
Patrick V. Haggerty
Keyword(s):  
Abelian Groups ◽  
Cohomology Algebra ◽  
Homotopy Types ◽  
Proper Homotopy ◽  
Open Formula

We give explicit examples of pairs of one-ended, open [Formula: see text]-manifolds whose end-sums yield uncountably many manifolds with distinct proper homotopy types. This answers strongly in the affirmative a conjecture of Siebenmann regarding nonuniqueness of end-sums. In addition to the construction of these examples, we provide a detailed discussion of the tools used to distinguish them; most importantly, the end-cohomology algebra. Key to our Main Theorem is an understanding of this algebra for an end-sum in terms of the algebras of summands together with ray-fundamental classes determined by the rays used to perform the end-sum. Differing ray-fundamental classes allow us to distinguish the various examples, but only through the subtle theory of infinitely generated abelian groups. An appendix is included which contains the necessary background from that area.

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