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The connective K theory of semidihedral groups

By Kijti Rodtes

Abstract

The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8)

Publisher: School of Mathematics and Statistics (Sheffield)
Year: 2010
OAI identifier: oai:etheses.whiterose.ac.uk:1103

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Citations

  1. (1998). A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture,
  2. (1993). A stable version of the Gromov-Lawson conjecture, The Cech centennial
  3. (2001). A user's Guide to Spectral Sequence, Cambridge studies in advance mathematics,
  4. (2002). Algebraic topology,
  5. (1961). Character and cohomology of ¯nite groups,
  6. (1974). Characteristic classes, Annals of Mathematics Studies,
  7. (1991). Classi¯cation of BG for groups with dihedral or quaternion Sylow 2-subgroups,
  8. (2004). Commutaive algebra in the Cohomology of Groups, Trens in Commutative Algrbra,
  9. (1999). Conditionally Convergent Spectral Sequences,
  10. (2010). Connective real K-theory of ¯nite groups,
  11. (2004). Equivariant connective K-theory for compac Lie groups,
  12. (1969). Equivariant K-theory and completion,
  13. (2005). Equivariant versions of real and complex connective K-theory, Homology,
  14. (1978). Homology of classical groups over ¯nite ¯elds,
  15. (1969). Introduction to Commutative Algebra, AddisonWesley series in mathematics,
  16. (1969). Lectures on Lie Groups, The
  17. (2007). Lectures on Local cohomology, Interactions between homotopy theory and algebra,
  18. (1977). Linear Representations of Finite Groups, Graduate Texts in Mathematics,
  19. (2002). Local cohomology in equivariant topology,
  20. (1996). Prime ideals and radicals in simigroup-graded rings,
  21. (1994). Real Connective K-theory of Finite groups, Thesis,
  22. (2004). Representations and cohomology, II: Cohomology of groups and modules, Cambridge studies in advanced mathematics,
  23. (1985). Representations of Compact Lie Groups,
  24. (1969). representations, ¸-ring and the
  25. (1974). Stable Homotopy and Generalised Homology, Chicago Lectures in Mathematics,
  26. T.Marley (note by L.Lynch), Introduction to local cohomology,
  27. (1981). The Bockstein and the Adams spectral sequences,
  28. (1985). The cohomology of the semi-dihedral group,
  29. (2003). The Connective K-Theory of Finite Groups,
  30. The Gromov-Lawson-Rosenberg conjecture for the Semi-dihedral group of order 16, (In
  31. The mod-2 cohomology of 2-groups,
  32. (1971). The mod-2 cohomology ring of extra-special 2-groups and the spinor groups,
  33. Vector Bundles and K-Theory,

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