scholarly journals The Persistent Morse Complex Segmentation of a 3-Manifold

2009 ◽  
pp. 36-50 ◽  
Author(s):  
Herbert Edelsbrunner ◽  
John Harer
Keyword(s):  
Morse Complex

scholarly journals On the automorphism group of the Morse complex

2021 ◽  
Vol 131 ◽  
pp. 102250
Author(s):  
Maxwell Lin ◽  
Nicholas A. Scoville
Keyword(s):  
Automorphism Group ◽  
Morse Complex

scholarly journals Linking and the Morse complex

2014 ◽  
Vol 23 (1) ◽  
pp. 25-94
Author(s):  
Michael Usher
Keyword(s):  
Morse Complex

SegMo: CT volume segmentation using a multi-level Morse complex

2019 ◽  
Vol 107 ◽  
pp. 23-36 ◽  
Author(s):  
Yukie Nagai ◽  
Yutaka Ohtake ◽  
Hiromasa Suzuki
Keyword(s):  
Volume Segmentation ◽  
Multi Level ◽  
Morse Complex ◽  
Ct Volume

Discrete Morse complex of images

2013 ◽  
Author(s):  
Ricardo Dutra da Silva
Keyword(s):  
Morse Complex

On the morse complex

1984 ◽  
Vol 187 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Xiao-Wei Peng
Keyword(s):  
Morse Complex

scholarly journals A Morse complex on manifolds with boundary

2010 ◽  
Vol 153 (1) ◽  
pp. 47-57 ◽  
Author(s):  
François Laudenbach
Keyword(s):  
Manifolds With Boundary ◽  
Morse Complex

scholarly journals A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES

2013 ◽  
Vol 15 (02) ◽  
pp. 1250059 ◽  
Author(s):  
MICHAEL B. HENRY ◽  
DAN RUTHERFORD
Keyword(s):  
Standard Form ◽  
Geometric Interpretation ◽  
Graded Algebra ◽  
Legendrian Knots ◽  
Complex Sequence ◽  
Differential Graded Algebra ◽  
Legendrian Knot ◽  
Definition Of ◽  
Morse Complex ◽  
Differential Counts

For a Legendrian knot L ⊂ ℝ3, with a chosen Morse complex sequence (MCS), we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MCS arises from a generating family F, we give a geometric interpretation of our chord paths as certain broken gradient trajectories which we call "gradient staircases". Given two equivalent MCS's we prove the corresponding linearized complexes of the DGA are isomorphic. If the MCS has a standard form, then we show that our DGA agrees with the Chekanov–Eliashberg DGA after changing coordinates by an augmentation.

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