a rapid course in morse homology - msri 2.pdf · from morse homology to floer homologya rapid...

51

Lecture 2. From Morse homology to Floer homology A rapid course in Morse homology A rapid course in Morse homology Let X be a smooth compact manifold of dimension d , and let f : X → R be a smooth function.

Upload: others

Post on 01-Jun-2020

5 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

Molecular homology

Waseda International Symposium · 2020. 2. 2. · Sakamoto and Yasutaka Shimizu) Yuan Wang Title: Group Analysis of Multi-Trial Brain Signals via Persistent Morse Homology Abstract:

Homology Groups And Persistence Homology. Outline Introduction Simplicial Complex Boundary Operator Homology Triangulation Persistent Homology 2

Class 8: Cech Homology, Homology of Relations, Relative Homology … › ... › s19-eat-notes-apr4.pdf · 2019-04-06 · Class 8: Cech Homology, Homology of Relations, Relative Homology

Homology modelling

Homology Theory, Morse Theory, and the Morse Homology …€¦ · Homology Theory, Morse Theory, and the Morse Homology Theorem Alex Stephanus June 8, 2016 Abstract This thesis develops

6. Morse Theory and Floer Homology - University of Texas ... › users › dafr › M392C-2018-MorseTheory … · 294 6. Morse Theory and Floer Homology p p p p p 1 1 f 2 p 1 2 3

Stratiﬁed Morse Theory: Past and Present › Massey › Massey_preprints › ... · Theory [15] and Morse Theory and Intersection Homology Theory [14], which contained announcements

Android Interactive Learning Morse App [Learn Morse] Morse Detailed Insrtuctions.pdfAndroid Interactive Learning Morse App [Learn Morse] Version v1.0 - April 2015 Introduction: Caution!

Khovanov Homology And Gauge Theoryianagol/MF60/talks/BerkeleyKhovanovHa… · To do Morse theory, we have to make two immediate changes. First, a Morse function is supposed to be

Discrete Morse Theory - 2012acat2012.dm.unibo.it/slides/mramorkosta.pdf · Smooth Morse functions Discrete Morse functions Applications References References: I Milnor, Morse theory,

Homology Groups And Persistence Homology

MATROID FILTRATIONS AND COMPUTATIONAL PERSISTENT …ghrist/preprints/Eirene.pdf · 2016-06-01 · homology, computational homology, and (elementary) discrete Morse theory: as such,

Different Approaches to Morse-Bott HomologyI John Milnor, Lectures on the h-cobordism theorem, Princeton University Press, 1965. I Matthias Schwarz, Morse homology, Progress in Mathematics

MORSE HOMOLOGY, TROPICAL GEOMETRY, AND HOMOLOGICAL … · MORSE HOMOLOGY, TROPICAL GEOMETRY, AND HOMOLOGICAL MIRROR SYMMETRY FOR TORIC VARIETIES MOHAMMED ABOUZAID Abstract. Given

Morphological Homology Molecular homology Fine anatomy Gross anatomy

HOMEWORK 1. - Peoplepeople.maths.ox.ac.uk/ritter/morse-cambridge/hwks.pdf · HOMEWORK 1. PART III, MORSE HOMOLOGY, 2011 HTTP://MORSEHOMOLOGY.WIKISPACES.COM Background: Consider the

Homology modelling ? X-ray ? NMR ?. Homology Modelling !

Discrete Morse Theory and Persistent Homologyhironaka/FSUUF/knudson.pdf · 2013-02-25 · Discrete Morse Theory Persistent Homology Persistence vs. DMT De nitions Gradients The Associated

Morse and Morse-Bott Homology - Pennsylvania State University · I Liviu Nicolaescu, An Invitation to Morse Theory, Universitext, Springer 2007. I Matthias Schwarz, Morse homology,

Different Approaches to Morse-Bott Homology · I Augustin Banyaga and David Hurtubise, Lectures on Morse homology, Kluwer Texts in the Mathematical Sciences 29, Kluwer Academic Publishers

Approximating Persistent Homology with Discrete Morse Theory · 2019-08-07 · Approximating Persistent Homology with Discrete Morse Theory Arkadi Schelling 12 University of Bremen

A Functional Analytic Approach to Morse Homologywendl/pub/Fowdar.pdfA Functional Analytic Approach to Morse Homology Author: Udhav Fowdar Supervisor: Dr. Chris Wendl 4th Year Mathematics

Homology Review

Morse Spectra, Homology Measures, Spaces of Cycles and ...gromov/wp-content/uploads/... · P ⊂ be a subspace invariant under this action. We are especially interested in those homotopy

Contents · This geometric theory developed further in the intersection homology and strati ed Morse the-ory of Goresky & MacPherson in [GM1], [GM2], and [GM3]. Their work continues

Cancer Associated E17K Mutation Causes Rapid Conformational … · 2017. 7. 15. · Cancer Associated E17K Mutation Causes Rapid Conformational Drift in AKT1 Pleckstrin Homology (PH)

PERTURBED GRADIENT FLOW TREES AND A -ALGEBRA … · treatments include [Nic11], [Mat02] and Chapter 6 of [Jos08]. There are also certain references specializing on Morse homology

A MORSE-BOTT APPROACH TO CONTACT HOMOLOGY

homology modeling

Morse Homology for the Yang-Mills Gradient Flo › ~swoboda › Swoboda_2012.pdf · such a Morse-Bott theory and the underlying L2 gradient ﬂow (2). The present article aims to

CALCULATING PERSISTENT HOMOLOGY USING DISCRETE …math.uchicago.edu/~may/REU2018/REUPapers/Lingareddy.pdfCALCULATING PERSISTENT HOMOLOGY USING DISCRETE MORSE THEORY 5 1) If a < f(p),

Computing Persistent Homology via Discrete Morse …moller/students/brian_brost.pdf · Computing Persistent Homology via Discrete Morse Theory ... topological data analysis, ... possible

Harker Gudhi 2014 - Inria · • Induced Homology on Maps (if time permits) Harker, Shaun, Konstantin Mischaikow, Marian Mrozek, and Vidit Nanda. "Discrete Morse theoretic algorithms