Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMG1004 | Morse Theory |
| Teaching Staff in Charge |
Assoc.Prof. PINTEA Cornel, Ph.D., cpintea math.ubbcluj.ro |
| Aims |
|
he course presents the basic facts of Morse theory and some of its applications both for real valued and circular valued functions. Specifically, we pay some attention towards the spherical homotopic structure of differential manifolds and the Morse inequalities, as well as the Morse complex of a real valued Morse function and the Novikov complex of a circular Morse function. |
| Content |
|
I. ELEMENTS OF HOMOLOGY
1.1 Chain complexes 1.2 The homology of chain complexes 1.3 Exact sequences 1.4 Betti numbers. Euler-Poincare characteristic II. BASES OF MORSE THEORY 1.1 The Morse lemma 1.2 Passing a critical level 1.3 The spheric homotopic structure of manifolds 1.4 Morse inequalities III. THE MORSE COMPLEX OF A MORSE FUNCTION 3.1 The Morse complex for tranversal gradients 3.2 The Morse complex for almost tranversal gradients 3.3 The chain Morse equivalence IV CIRCLE-VALUED MORSE MAPS AND NOVIKOV COMPLEXES 4.1 Completions of rings, modules and complexes 4.2 Chain complexes over A[[t]] 4.3 The Novikov comnplex of a circle-valued Morse map |
| References |
|
1. Burghelea D., Hangan, Th., Moscovici, H., Verona, A., Introducere in Topologia
Diferentiala, Editura Stiintifica, Bucuresti 1973. 2. Pajitnov, A.V., Circle-valued Morse Theory, Walter de Gruyter, 2006 3. Pintea, C., Geometrie. Geometrie Diferentiala. Geometrie Riemanniana. Grupuri si Algebre Lie, Presa Universitara Clujeana, 2006 |
| Assessment |
|
Exam+Quiz+Reports |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |