# Publications of Nicholas J. Kuhn

Books edited

1. (with J.P.C.Greenlees and R.R.Bruner) Homotopy Methods in Algebraic Topology, Proceedings of the 1999 Conference in Boulder, A. M. S. Cont. Math. Series 271, 2001.

Research Papers

All papers since 2002 are available in preprint form at arxiv.org. Many older papers are also available on one or more of the following archives: the Hopf archive at https://hopf.math.purdue.edu, the K–theory archive at https://faculty.math.illinois.edu/K-theory, or the group cohomology archive at https://homepages.abdn.ac.uk/d.j.benson/pages/html/archive.html.

1. The geometry of the James-Hopf Maps, Pac. J. Math. 102 (1982), 397–412.

2. (with S.A.Mitchell and S.B.Priddy) The Whitehead conjecture and splitting $$B(\mathbb Z/2)^k$$, Bull. A. M. S. 7 (1982), 255–258.

3. A Kahn-Priddy sequence and a conjecture of G.W.Whitehead, Math. Proc. Camb. Phil. Soc. 92 (1982), 467–483. (Corrigenda, 95(1984), 189–190.)

4. (with F.R.Cohen, R.L.Cohen, and J.L.Neisendorfer)  Bundles over configuration spaces, Pac. J. Math. 104 (1983), 47–54.

5. The homology of the James-Hopf maps, Ill. J. Math. 27 (1983), 315–333.

6. Spacelike resolutions of spectra, Northwestern Homotopy Theory Conference, Proc. Evanston, 1982, A. M. S. Cont. Math. Series 19 (1983), 153–165.

7. Suspension spectra and homology equivalences, Trans. A. M. S. 283 (1984), 303–313.

8. (with an appendix by P.Landrock) The modular Hecke algebra and Steinberg representation of finite Chevalley groups, J. Algebra 91 (1984), 125–141.

9. Extended powers of spectra and a generalized Kahn-Priddy Theorem, Topology 23 (1985), 473–480.

10. Chevalley group theory and the transfer in the homology of symmetric groups, Topology 24 (1985), 247–264.

11. (with S.B.Priddy)  The transfer and Whitehead’s conjecture, Math. Proc. Camb. Phil. Soc. 98 (1985), 459–480.

12. (with S.A.Mitchell)  The multiplicity of the Steinberg representation of $$GL_n(\mathbb F_q)$$ in the symmetric algebra, Proc. A. M. S. 96(1986), 1–6. 1

13. Exact sequences of spectra and duality, Proc. A. M. S. 97 (1986), 347–351.

14. The mod p K-theory of classifying spaces of finite groups, J. Pure Appl. Alg. 44 (1987), 269–271.

15. The rigidity of L(n), Algebraic Topology – Seattle 1985, Springer Lect. Notes Math. 1286 (1987), 286–292.

16. The Morava K-theories of some classifying spaces, Trans. A. M. S. 304 (1987), 193– 205.

17. The transfer and James-Hopf invariants, Math. Zeit. 196 (1987), 391–405.

18. (with J.C.Harris) Stable decompositions of classifying spaces of finite abelian p-groups, Math. Proc. Camb. Phil. Soc. 103 (1988), 427–449.

19. Morava K-theories and infinite loop spaces, Algebraic Topology, Proc. Arcata, 1986, Springer Lect. Notes Math. 1370 (1989), 243–257.

20. (with D.Carlisle) Subalgebras of the Steenrod algebra and the action of matrices on truncated polynomial algebras, J. Algebra 121 (1989), 370–387.

21. (with D.Carlisle) Smash products of summands of $$B(\mathbb Z/p)^n_+$$, Northwestern Topology Conference, Proc. Evanston, 1988, A. M. S. Cont. Math. Series 96 (1989), 87–102.

22. Character rings in algebraic topology, Advances in Homotopy Theory, Proc. Cortona 1988, L. M. S. Lectures Notes 139 (1989), 111–126.

23. (with J. F. Adams)  Atomic spaces and spectra, Proc. Edin. Math. Soc. 32 (1989), 473–481.

24. (with M.J.Hopkins and D.C.Ravenel)  Morava K-theories of classifying spaces and generalized characters for finite groups, Topology Conference, Proc. Barcelona, 1990, Springer Lecture Notes in Math. 1509 (1992), 186–209.

25. Generic representation theory and Lannes’ T-functor, Adams Memorial Symp., Proc. Manchester, 1990, L. M. S. Lecture Notes 176 vol.2 (1992), 235–262.

26. (with Jeanne Duflot and Mark Winstead)  A classification of polynomial algebras as modules over the Steenrod algebra, Comm. Math. Helv. 68 (1993), 622–632.

27. (with Piotr Krason)  On embedding polynomial functors in symmetric powers, J.Algebra 163 (1994), 281–294.

28. Constructions of families of elements in the stable homotopy groups of spheres, Topology and Representation Theory, Proc. Evanston, 1992, A.M.S. Cont. Math. 158 (1994), 135–155. 2

29. Morita equivalence, GL(n,q) modules, and the Steenrod algebra, Algebraic Topology and its Applications, Proc. Berkeley, 1989, M.S.R.I. Pub. 27 (1994), 125–137.

30. Generic representations of the finite general linear groups and the Steenrod algebra:I, Amer. J. Math. 116 (1994), 327–360.

31. Generic representations of the finite general linear groups and the Steenrod algebra:II, K-theory J. 8 (1994), 395–428.

32. Generic representations of the finite general linear groups and the Steenrod algebra:III, K-theory J. 9 (1995), 273–303.

33. On topologically realizing modules over the Steenrod algebra, Annals of Math. 141 (1995), 321–347.

34. (with M. Slack and F.Williams)  Hopf constructions and higher projective planes for iterated loop spaces, Trans. A.M.S. 347 (1995), 1201–1238.

35. (with M. Winstead)  On torsion in the cohomology of certain mapping spaces, Topology 35 (1996), 875–881.

36. Invariant subspaces of the ring of functions on a vector space over a finite field, J. Algebra 191 (1997), 212–227.

37. Computations in generic representation theory: maps from symmetric powers to composite functors, Trans. A.M.S.350 (1998), 4221–4233.

38. Rational cohomology and cohomological stability in generic representation theory, Amer. J. Math.120 (1998), 1317–1341.

39. (with D. J. Hunter)  Mahowaldean families of elements in stable homotopy groups revisited, Math. Proc. Camb. Phil. Soc. 127 (1999), 237–251.

40. (with D. J. Hunter)  Characterizations of spectra with U-injective cohomology which satisfy the Brown–Gitler property, Trans. A.M.S.352 (2000), 1171–1190.

41. (with M.J.Hopkins and D.C.Ravenel)  Generalized group characters and complex oriented cohomology theories, Journal A.M.S.13 (2000), 553–594.

42. The generic representation theory of finite fields: a survey of basic structure, Infinite Length Modules, Proc. Bielefeld, 1998, Trends in Mathematics, Birkhauser (2000), 193–212.

43. New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces, Cohomological Methods in Homotopy Theory, Proc. Barcelona, 1998, Birkhauser Verlag Progress in Math 196(2001), 185–216. 3

44. Splitting fields and twisted group rings for the finite general linear groups, Modular Representation Theory of Finite Groups, Proc. Charlottesville, 1998, de Gruyter (2001), 231–237.

45. Stable splittings and the diagonal, Homotopy Methods in Algebraic Topology, Proc. Boulder, CO, 1999, A.M.S. Cont. Math. 271 (2001), 169–181.

46. A stratification of generic representation theory and generalized Schur algebras, K-theory J. 26 (2002), 15–49.

47. (with S.T.Ahearn) Product and other fine structure in polynomial resolutions of mapping spaces, Algebraic and Geometric Topology 2 (2002), 591–647.

48. The McCord model for the tensor product of a space and a commutative ring spectrum, Categorical Decomposition Techniques in Algebraic Topology, Proc. Isle of Skye, Scotland, 2001, Birkhauser Verlag Progress in Math 215 (2003), 213–236.

49. Tate cohomology and periodic localization of polynomial functors, Invent. Math. 157 (2004), 345–370.

50. Localization of Andr´e–Quillen–Goodwillie towers, and the periodic homology of infinite loopspaces, Advances in Math. 201 (2006), 318–378.

51. Mapping Spaces and Homology Isomorphisms, Proc. A.M.S. 134 (2006), 1237–1248. With an appendix joint with G. Arone.

52. Goodwillie towers and chromatic homotopy: an overview, Algebraic Topology, Proc. Kinosaki, Japan, 2003, Geometry and Topology Monographs 10 (2007), 245–279.

53. Primitives and central detection numbers in group cohomology, Advances in Math. 216 (2007), 387–442.

54. The nilpotent filtration and the action of automorphisms on the cohomology of finite p–groups, Math. Proc. Camb. Phil. Soc. 144 (2008), 575–602.

55. A guide to telescopic functors, Johns Hopkins Conference on Algebraic Topology, Proc. Baltimore, 2007, Homology, Homotopy, and Applications 10 (2008), 291–319.

56. Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology, Algebraic and Geometric Topology 8 (2008), 2109–2129. (Correction: 10 (2010), 531–533.)

57. Nilpotence in group cohomology, Proc. Edin. Math. Soc. 56 (2013), 151–175.

58. (with J. B. McCarty) The mod 2 homology of infinite loopspaces, Algebraic and Geometric Topology 13 (2013), 687–745. 4

59. The Krull filtration of the category of unstable modules over the Steenrod algebra, Math. Zeit. 277 (2014), 917–936.

60. The Whitehead Conjecture, the Tower of $$S^1$$ Conjecture, and Hecke algebras of type A, J. Topology 8 (2015), 118–146.

61. Generic representation theory of finite fields in nondescribing characteristic, Advances in Math. 272 (2015), 598–610.

62. (with Luis A. Pereira)  Operad bimodules, and composition products on Andr´e–Quillen filtrations of algebras, Algebraic and Geometric Topology 17 (2017), 1105–1130.

63. Adams filtration and generalized Hurewicz maps for infinite loopspaces, Invent. Math. 214 (2018), 957--998.

64.  Hopf algebras, quasi-shuffle algebras and the cohomology of $$\Omega \Sigma X$$Advances in Math. 369 (2020), 107013, 30pp.

65. (with Chris J.R.Lloyd)  Chromatic fixed point theory and the Balmer spectrum for extraspecial 2--groups, preprint, 2020.

Reports and other miscellaneous publications

1. Cohomology primitives associated to central extensions, Oberwolfach Reports 2 (2005), 2383–2386.

2. (with Carles Broto,, Nguyen H. V. Hung, John H. Palmieri, Stewart Priddy, and Nobuaki Yagita) The problem session. Proc. School and Conference in Algebraic Topology, Hanoi, 2004, Geometry and Topology Monographs 11 (2007), 435–441.

3. Adams filtration and infinite loopspaces, Oberwolfach Reports 4 (2007), 2703–2705.

4. Restriction to the center in group cohomology, Oberwolfach Reports 7 (2010), 1919– 1922.

5. The mod 2 homology of infinite loopspaces, Oberwolfach Reports 8 (2011), 2660–2663.

6. Generic representations of finite fields in nondescribing characteristic, Oberwolfach Reports 12 (2015), 1377–1379.

7. New results about the equivariant stable homotopy Balmer spectrum, Oberwolfach Reports 16  (2019).