Papers, talks and computer code of Robert R. Bruner

• Computer code
• Talks
• Notes
• Publications

Computer Code

• FP_Modules
  SAGE code to compute with finitely presented modules over the mod p Steenrod algebra, any p. Written by Mike Catanzaro. You can define finitely presented modules and homomorphisms between them. You can compute kernels, images, cokernels, direct sums, resolutions, and modules defined by elements of Ext^1.
  
  
• Chern
  MAGMA code to compute Chern classes. Set G to the group you want and "load Chern;". It will print the character table and then report the Chern clases of each irreducible, both as a character and as a linear combination of the irreducibles.
  Sample output: Dihedral of order 16 and Alternating on 5 letters.
  
  
• Dyer-Lashof
  MAGMA code to compute the mod 2 cohomology of the r^th extended power of a spectrum. Input is a module over the mod 2 Steenrod algebra in the 'module definition format'. Set
  • N to be the upper limit of the calculation; we will compute the N-skeleton in other words,
  • r to indicate the r^th extended power, and
  • file to the name of the file containing the description of the input module.
  It will write the output in a file named D_rfiletoNmod (substitute r, file and N that you set) which is in the module defintion format so that it can be fed directly into the newmodule command of the ext package. The variable Mons will be useful in interpreting that file. See some sample runs to see the calculation of the module definition for for the 7 skeleton of D_2(S^1) and for the 10 skeleton of D_2 of this 6 cell complex. Here is the Ext chart for the 40 (rather than 10) skeleton of the D_2(D_2^7(S^1)) produced by ext.1.8.3 while I was typing this up. (1 min.) From it you can see, for example, that pi_4,5,6,7 are each Z/2, with pi_4,5,6 mapping monomorphically under the Hurewicz map and with nu acting nontrivially on all three of these.
  
  
• Ext.1.8.3
  The latest stable version of the ext calculator.

Talks

• The Finiteness Conjecture
       at the Workshop on the Kervaire invariant and stable homotopy theory, 28 April 2011.
• Characteristic Classes in Connective K-Theory ( Part 1 and Part 2 )
       University of Muenster, Oberseminar Topologie, 20 June 2011.
• Commutative Ring Spectra and Spectral Sequences
       at the Conference on Structured Ring Spectra, in Hamburg, 1-5 August 2011.
• The Finiteness Conjecture
       Topology Seminar, Universitetet i Bergen, 9 August 2011. (Quite similar to Edinburgh talk.)
• Characteristic Classes in Connective K-Theory ( General Theory and Compact Lie Groups )
       Topology Seminar, Universitetet i Bergen, 10 August 2011. (Substantially reorganized since the Muenster talk. Still too long.)

Notes

Publications

• Radicals and Torsion Theories in Locally Compact Groups, undergraduate thesis, Amherst College, Dec 1972.
• Two Generalizations of the Adams Spectral Sequence, Canadian Mathematical Society Conference Proceedings, V. 2, part 1 (1982) pp. 275--287.
• The Connective K-theory of Finite Groups (with John Greenlees) (prepublication version of Memoirs AMS V. 165 N0. 785 Sept 2003)
  
• On the behavior of the algebraic transfer, Robert R. Bruner; Le Minh Ha; Nguyen H. V. Hung, Trans. Amer. Math. Soc. 357 (2005), 473-487. dvi , ps , pdf .
• Extended powers of manifolds and the Adams spectral sequence dvi pdf
  Homotopy methods in algebraic topology (Boulder, CO, 1999), Contemp. Math. 271 , Amer. Math. Soc., Providence, RI, 2001, 41--51,
• Ossa's Theorem and Adams covers
  Proc. Amer. Math. Soc. 127 (1999), no. 8, 2443--2447.
• Some Remarks on the Root Invariant
  (Stable and Unstable Homotopy (Toronto, ON 1996), Fields Inst. Commun. 19 , 1998, 31-37)
• A Yoneda Description of the Steenrod Operations
  ( Proc. Symp. Pure Math. 63 (1998), problem session)
• Some root invariants and Steenrod operations in Ext_A(F2,F2)
  ( Contem. Math., 220 (1997), 27-33.)
• Real connective K-theory and the quaternion group (with Dilip Bayen) dvi
  (Trans. AMS 348 (1996), 2201-2216.)
• On stable homotopy equivalences (with F. R. Cohen and C. A. McGibbon)
  (Oxford Quarterly J. of Math., (2) 46 (1995), 11-20.)
• The Bredon-Loffler conjecture (with J. P. C. Greenlees)
  (Exper. Math. 4 (1995), 289-297.)
• Ext in the nineties
  ( Contemp. Math., 146 (1993), 71-90.)

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Cohomology charts