Papers, talks and computer code of Robert R. Bruner

Cohomology charts

Visualization of A(2)

Computer Code



  1. A Counterexample for lightning flash modules over E(e1,e2)
    Archiv der Mathematik, 23 Feb. 2016, DOI 10.1007/s00013-016-0880-8.

  2. Idempotents, Localizations and Picard Groups of A(1)−modules
    in An Alpine Expedition through Algebraic Topology, Contemporary Mathematics, vol. 617, Amer. Math. Soc., Providence, RI, 2014, pp. 81-108.
    ( (Formerly On Ossa's Theorem and Local Picard Groups, arXiv:1211.0213.)

  3. On cyclic fixed points of spectra (with Marcel Bokstedt, Sverre Lunoe-Nielsen, and John Rognes)
    Math. Zeit. 11 July 2013, (DOI) 10.1007/s00209-013-1187-0

  4. Connective real K-theory of finite groups (with John Greenlees),
    Mathematical Surveys and Monographs 169, Amer. Math. Soc., Providence, RI 2010.

  5. Differentials in the homological homotopy fixed point spectral sequence (with John Rognes),
    Algebr. Geom. Topol. 5, 653--690 (electronic) 2005.

  6. On the behavior of the algebraic transfer, (with Le Minh Ha and Nguyen H. V. Hung)
    Trans. Amer. Math. Soc. 357, 473--487 2005.

  7. The Connective K-theory of Finite Groups (with John Greenlees),
    prepublication version of Memoirs AMS V. 165 No. 785, Sept 2003.

  8. Nonimmersions of real projective spaces implied by tmf (with Donald M. Davis and Mark Mahowald),
    Recent progress in homotopy theory (Baltimore, MD, 2000)
    Contemp. Math. 293, 45--68, Amer. Math. Soc., Providence, RI 2002.

  9. Extended powers of manifolds and the Adams spectral sequence ,
    Homotopy methods in algebraic topology (Boulder, CO, 1999),
    Contemp. Math. 271, 41--51, Amer. Math. Soc., Providence, RI 2001.

  10. Homotopy methods in algebraic topology (ed. with J. P. C. Greenlees and Nicholas Kuhn),
    Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Colorado, Boulder, CO, June 20–24, 1999.
    Contemporary Mathematics 271, Amer. Math. Soc., Providence, RI 2001.

  11. Ossa's Theorem and Adams covers
    Proc. Amer. Math. Soc. 127 (1999), no. 8, 2443--2447.

  12. Some root invariants and Steenrod operations in Ext_A(F2,F2)
    Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997),
    Contemp. Math. 220, 27--33, Amer. Math. Soc., Providence, RI, 1998.

  13. Some Remarks on the Root Invariant
    Stable and Unstable Homotopy (Toronto, ON 1996), Fields Inst. Commun. 19 (1998) 31--37.
    Correction: at the bottom of page 3, the element mu is in pi_9, not pi_8.

  14. A Yoneda Description of the Steenrod Operations
    Proc. Symp. Pure Math. 63 (1998), problem session.

  15. Real connective K-theory and the quaternion group (with Dilip Bayen)
    Trans. AMS 348 (1996), 2201-2216.

  16. On stable homotopy equivalences (with F. R. Cohen and C. A. McGibbon)
    Oxford Quarterly J. of Math., (2) 46 (1995), 11-20.

  17. The Bredon-Loffler conjecture (with J. P. C. Greenlees)
    Exper. Math. 4 (1995), 289-297.

  18. On recursive solutions of a unit fraction equation (with Lawrence Brenton)
    J. Austral. Math. Soc. Ser. A 57 (1994), no. 3, 341--356.

  19. Ext in the nineties
    Contemp. Math., 146 (1993), 71-90.

  20. Calculation of large Ext modules
    Computers in geometry and topology (Chicago, IL, 1986),
    Lecture Notes in Pure and Appl. Math., 114 79--104, Marcel Dekker, New York, 1989.

  21. An example in the cohomology of augmented algebras
    J. Pure Appl. Algebra 55 (1988), no. 1-2, 81--84.

  22. H_infinity ring spectra and their applications (with J. P. May, J. E. McClure and M. Steinberger)
    Lecture Notes in Mathematics, 1176. Springer-Verlag, Berlin, 1986. (Peter's copy)

  23. A new differential in the Adams spectral sequence
    Topology 23 (1984), no. 3, 271--276.

  24. Two Generalizations of the Adams Spectral Sequence
    Canadian Mathematical Society Conference Proceedings, V. 2, part 1 (1982) pp. 275--287.

  25. An infinite family in pi*(S^0) derived from Mahowald's eta-j family
    Proc. Amer. Math. Soc. 82 (1981), no. 4, 637--639.

  26. Algebraic and geometric connecting homomorphisms in the Adams spectral sequence
    Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, pp. 131--133.
    Lecture Notes in Math., 658, Springer, Berlin, 1978.

  27. Locally compact groups without distinct isomorphic closed subgroups (with D. L. Armacost)
    Proc. Amer. Math. Soc. 40 (1973), 260--264.

  28. Radicals and Torsion Theories in Locally Compact Groups
    undergraduate thesis, Amherst College, Dec 1972.


  1. Ossa's Theorem via the Kunneth formula (with Khairia Mira, Laura Stanley and Victor Snaith)

  2. On the Postnikov towers for real and complex connective K-theory


  1. The tangent bundle of projective space
    Uses equivariance to compute the tangent bundles of real and complex projective spaces as an alternative to the argument given in Milnor and Stasheff. It is more direct and explicit.

  2. The Cohomology of ku
    An account of Adams' calculation of the mod 2 cohomology of complex connective K-theory.

  3. The Cohomology of the mod 2 Steenrod Algebra
    Results of the penultimate run, complete with all products, out to t=141, s=40. The exposition is a very rough draft, but the results should be correct.

  4. An Adams Spectral Sequence primer
    A draft of an introduction to the classical Adams spectral sequence.

  5. The connective complex K-theory of an elementary abelian p-group
    A note written to answer a question asked about the rank 3 case at an odd prime. Contains some general remarks about all ranks.

  6. How to solve a quartic

  7. Asymmetry and efficiency in Toda brackets
    I show that computing Toda brackets via Yoneda composites requires less data than might be expected. This is useful in doing actual computations.

  8. Cup 1 and symmetric Toda brackets
    Derivation of the formula for a symmetric 3-fold Toda bracket in terms of cup-1 operations, valid when cup-1 satisfies the Hirsch formula.

  9. A Relation in the Steenrod Algebra
    The Adem relation needed to reduce all squaring operations to those given by a power of 2.

  10. Some squaring operations in Ext
    Calculated by machine, using every tool available.

  11. The semi-dihedral algebra in algebraic topology
    Why the 8 dimensional semi-dihedral algebra is of interest to algebraic topologists.

  12. Tate Cohomology of the anto-involution of the Steenrod algebra
    Calculated by MAGMA, in the effort to gather further data on the questions remaining after the paper by Crossley and Whitehouse (Proc AMS 2000).

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