• About
  • Policies
  • What is open access
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Mathematics
      • Dept. of Mathematics - Ph.D. / Sc.D.
      • View Item
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Mathematics
      • Dept. of Mathematics - Ph.D. / Sc.D.
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

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

      Thumbnail
      Embargo Lift Date: 2020-01-04
      View / Download
      607.8 Kb
      Author(s)
      Mutlu, Hatice
      Advisor
      Barker, Laurence John
      Date
      2019-06
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
      Item Usage Stats
      335
      views
      179
      downloads
      Abstract
      Green 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.
      Keywords
      Green functors
      P-permutation modules
      Canonical induction formula
      Burnside ring
      Monomial Burnside ring
      Tensor induction
      Lefschetz invariant
      Permalink
      http://hdl.handle.net/11693/52147
      Collections
      • Dept. of Mathematics - Ph.D. / Sc.D. 48
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCoursesThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCourses

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 2976
      © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy