GREBNEROVE BAZE ZA MNOGOSTRUKOSTI ZASTAVA I PRIMENE

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GREBNEROVE BAZE ZA MNOGOSTRUKOSTI ZASTAVA I PRIMENE

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dc.contributor.advisor Petrović, Zoran
dc.contributor.author Radovanović, Marko
dc.date.accessioned 2016-09-06T07:30:40Z
dc.date.available 2016-09-06T07:30:40Z
dc.date.issued 2015
dc.identifier.uri http://hdl.handle.net/123456789/4298
dc.description.abstract By Borel's description, integral and mod 2 cohomology of ag manifolds is a polynomial algebra modulo a well-known ideal. In this doctoral dissertation, Gr obner bases for these ideals are obtained in the case of complex and real Grassmann manifolds, and real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n). In the case of Grassmann manifolds, Gr obner bases are applied in the study of Z- cohomology of complex Grassmann manifolds. It is well-known that, besides Borel's description, this cohomology can be characterized in terms of Schubert classes. By establishing a connection between this description and Gr obner bases that we obtained, a new recurrence formula that can be used for calculating (all) Kostka numbers is derived. Using the same method for the small quantum cohomology of Grassmann manifolds (instead of the classical), these formulas are improved. In the case of real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n), Gr obner bases are used to obtain new results on the immersions and embeddings of these manifolds, and for the calculation of the cup-length of some manifolds of this type. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2016-09-06T07:30:40Z No. of bitstreams: 1 phdRadovanovic_Marko.pdf: 1476309 bytes, checksum: b2f429d1444b05fcab10939036765530 (MD5) en
dc.description.provenance Made available in DSpace on 2016-09-06T07:30:40Z (GMT). No. of bitstreams: 1 phdRadovanovic_Marko.pdf: 1476309 bytes, checksum: b2f429d1444b05fcab10939036765530 (MD5) Previous issue date: 2015 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title GREBNEROVE BAZE ZA MNOGOSTRUKOSTI ZASTAVA I PRIMENE en_US
mf.author.birth-date 1985-10-23
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Gr obner bases, cohomology of ag manifolds, quantum cohomology, symmetric functions, Kostka numbers, cup-length, Schubert calculus, Chern classes, Stiefel-Whitney classes, immersions en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee Lipkovski, Aleksandar
mf.contributor.committee Malešević, Branko
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Đanković, Goran
mf.contributor.committee Prvulović, Branislav
mf.university.faculty Mathematical Faculty en_US
mf.document.references 68 en_US
mf.document.pages 143 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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