Canonical induction, Green functors, lefschetz invariant of monomial G-posets

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buir.advisorBarker, Laurence John
dc.contributor.authorMutlu, Hatice
dc.date.accessioned2019-07-08T10:58:06Z
dc.date.available2019-07-08T10:58:06Z
dc.date.copyright2019-06
dc.date.issued2019-06
dc.date.submitted2019-06-04
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2019.en_US
dc.descriptionIncludes bibliographical references (leaves (101-102).en_US
dc.description.abstractGreen functors are a kind of group functor, rather like Mackey functors, but with a further multiplicative structure. They are defined on a category whose objects are finite groups and whose morphisms are generated by maps such as induction, restriction, inflation, deflation. The aim of this thesis is general formulation for canonical induction, suitable for Green functors, optionally equipped with inflations. Let p be a prime number. In Section 3, we apply the Boltje’s theory of canonical induction [1] to p-permutation modules and give a restriction-preserving Z[1/p]- linear canonical induction formula from the inflations of projective modules. In Section 4, we give a general formulation of canonical induction theory for Green biset functors equipped with induction, restriction, inflation maps. Let G be a finite group and C be an abelian group. In Section 5, motivated in part by a search for connection with Peter Symonds’ proof [2] of the integrality of a canonical induction formula, we introduce a Lefschetz invariant for the Cmonomial Burnside ring. These invariants let us to construct generalize tensor induction functors associated to any C-monomial (G, H)-biset from the category of C-monomial G-posets to the category of C-monomial H-posets. We will show that these functors induce well-defined tensor induction maps from BC(G) to BC(H), which in turn gives a group homomorphism BC(G) × → BC(H) × between the unit groups of C-monomial Burnside rings.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2019-07-08T10:58:06Z No. of bitstreams: 1 thesisHaticeMutlu.pdf: 622374 bytes, checksum: e2639826356b9f5ffbff9cbe8f7001d1 (MD5)en
dc.description.provenanceMade available in DSpace on 2019-07-08T10:58:06Z (GMT). No. of bitstreams: 1 thesisHaticeMutlu.pdf: 622374 bytes, checksum: e2639826356b9f5ffbff9cbe8f7001d1 (MD5) Previous issue date: 2019-06en
dc.description.statementofresponsibilityby Hatice Mutluen_US
dc.embargo.release2020-01-04
dc.format.extentvii, 102 leaves ; 30 cm.en_US
dc.identifier.itemidB153317
dc.identifier.urihttp://hdl.handle.net/11693/52147
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectGreen functorsen_US
dc.subjectP-permutation modulesen_US
dc.subjectCanonical induction formulaen_US
dc.subjectBurnside ringen_US
dc.subjectMonomial Burnside ringen_US
dc.subjectTensor inductionen_US
dc.subjectLefschetz invarianten_US
dc.titleCanonical induction, Green functors, lefschetz invariant of monomial G-posetsen_US
dc.title.alternativeKuralsal indüksiyon, Green izleçleri, tek terimli G-kısmi sıralı kümelerinin lefschetz değişmezlerien_US
dc.typeThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorBilkent University
thesis.degree.levelDoctoral
thesis.degree.namePh.D. (Doctor of Philosophy)

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