On the Orbits of Monodromy Action/ (Record no. 38715)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03137n a2200301#a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 40073 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | P5A |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20230123132000.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cuuuuuauuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210423s2021 bl por d |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | ocm51338542 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | P5A |
| Transcribing agency | P5A |
| 090 ## - IMPA CODE FOR CLASSIFICATION SHELVES | |
| IMPA CODE FOR CLASSIFICATION SHELVES | Teses do IMPA |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Garcia, Daniel Felipe López |
| 9 (RLIN) | 1182 |
| 245 10 - TITLE STATEMENT | |
| Title | On the Orbits of Monodromy Action/ |
| Statement of responsibility, etc. | Daniel Felipe López Garcia. |
| 246 11 - VARYING FORM OF TITLE | |
| Title proper/short title | Acerca das Órbitas da Ação de Monodromia |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | Rio de Janeiro: |
| Name of publisher, distributor, etc. | IMPA, |
| Date of publication, distribution, etc. | 2021. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | video online |
| 500 ## - GENERAL NOTE | |
| General note | Defesa de Tese. |
| 500 ## - GENERAL NOTE | |
| General note | Banca examinadora: Hossein Movasati - Orientador - IMPA Alcides Lins - IMPA Younes Nikdelan - UERJ Colin Christopher - Univ. Phymouth Lubomir Gavrilov - Université Toulouse Roberto Villaflor - Suplente - IMPA |
| 505 1# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Abstract: The monodromy action relates the topology of a parametrized family of manifolds with the fundamental group of the parameters space. There is a topological approach based on the Lefschetz fibrations. Given a smooth fibration, the action of the fundamental group of the base without the critical values on the homology group of a regular fiber is the monodromy action. In some cases, the homology group is generated by the so-called vanishing cycles; which are associated with the critical values of the fibration. Another method is by using Picard-Fuchs equations, whose solutions are the periods of some complex manifolds, and the monodromy action is obtained by holomorphic continuation around to the critical values. The first main part is related to symplectic geometry by studying the Lagrangian cycles in a family of mirror quintic Calabi-Yau threefolds. Considering a symplectic structure in a fibration such that the fibers are symplectic manifolds, it is possible to show that the vanishing cycles are Lagrangian submanifolds and the monodromy action is given by symplectomorphisms. In the case of mirror quintic, there is an explicit form for the monodromy matrices and for two Lagrangian cycles which are supported in a 3-sphere and 3-torus. We study the orbit of these cycles by monodromy action. The second main part is related to the monodromy problem in polynomial foliations. Given a polynomial with two variables we consider its associated foliation. The center points of the foliation are vanishing cycles. The monodromy problem is to establish conditions on the polynomial so the orbit of the vanishing cycles generate the whole homology group. It is possible to relate the monodromy action with a diagram called the Dynkin diagram. Thus, given a polynomial, we translate questions on the subspaces generated by these orbits to combinatory aspects of the diagram . |
| 650 04 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Matematica. |
| Source of heading or term | larpcal |
| 9 (RLIN) | 19899 |
| 697 ## - LOCAL SUBJECT | |
| Local Subject | Teses do IMPA |
| Linkage | 24311 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Movasati, Hossein |
| Affiliation | (IMPA) |
| Relator term | orientador |
| 9 (RLIN) | 13899 |
| 711 2# - ADDED ENTRY--MEETING NAME | |
| Meeting name or jurisdiction name as entry element | Defesa de Tese |
| 9 (RLIN) | 10070 |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Public note | VIDEO |
| Uniform Resource Identifier | <a href="https://bit.ly/2PbGyny">https://bit.ly/2PbGyny</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Instituto de Matemática Pura e Aplicada |
| Koha item type | VIDEO |
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