57 citations · 174 across the 24 of their papers we have counts for
22 papers · 1 filter
Applications of the circle product with a right -module to the theory of commutative ring spectra
Nicholas J. Kuhn
If Com is the reduced commutative operad, the category of Com-algebras in spectra is the category of nounital commutative ring spectra. The theme of this survey is that many import…
Type 2 complexes constructed from Brown-Gitler spectra
William Balderrama, Justin Barhite, Nicholas J. Kuhn +1
In a previous paper, one of us interpreted mod 2 Dyer-Lashof operations as explicit A-module extensions between Brown-Gitler modules, and showed these A-modules can be topologicall…
Dyer-Lashof operations as extensions of Brown-Gitler Modules
Nicholas J. Kuhn
At the prime 2, let T(n) be the n dual of the nth Brown-Gitler spectrum with mod 2 homology G(n). Our previous work on computing the homology of an infinite loopspaces led us to ob…
An elementary proof of the chromatic Smith fixed point theorem
William Balderrama, Nicholas J. Kuhn
A recent theorem by T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton says that if A is a finite abelian p-group of rank r, then any finite A-space X whic…
A short proof of the chromatic Smith Fixed Point Theorem
Nicholas J. Kuhn
We give a short and much simplified proof of the main theorem of the recent study, by T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton, of the Balmer spe…
Computing the Morava K-theory of real Grassmanians using chromatic fixed point theory
Nicholas J. Kuhn, Christopher J. R. Lloyd
We study K(n)*(Gr(d,m)) for all n - the 2-local Morava K-theories of the real Grassmanian Gr(d,m) of d-planes in R^m, about which very little has been previously computed. We conje…
Chromatic fixed point theory and the Balmer spectrum for extraspecial 2-groups
Nicholas J. Kuhn, Christopher J. R. Lloyd
In the early 1940's, P.A.Smith showed that if a finite p-group G acts on a finite complex X that is mod acyclic, then its space of fixed points, X^G, will also be mod p acyclic…
Operad bimodules, and composition products on Andre-Quillen filtrations of algebras
Nicholas J. Kuhn, Luis A. Pereira
If O is a reduced operad in symmetric spectra, an O-algebra I can be viewed as analogous to the augmentation ideal of an augmented algebra. Implicit in the literature on Topologica…
Adams filtration and generalized Hurewicz maps for infinite loopspaces
Nicholas J. Kuhn
We study the Hurewicz map h from the homotopy groups of a spectrum X to the R-homology of its 0th space X(0), where R is a connective commutative S-algebra. We prove that the decre…
The Whitehead Conjecture, the Tower of S^1 Conjecture, and Hecke algebras of type A
Nicholas J. Kuhn
In the early 1980's the author proved G.W. Whitehead's conjecture about stable homotopy groups and symmetric products. In the mid 1990's, Arone and Mahowald showed that the Goodwil…
The Krull filtration of the category of unstable modules over the Steenrod algebra
Nicholas J. Kuhn
In the early 1990's, Lionel Schwartz gave a lovely characterization of the Krull filtration of U, the category of unstable modules over the mod p Steenrod algebra. Soon after, this…
The mod 2 homology of infinite loopspaces
Nicholas J. Kuhn, Jason B. McCarty
We study the spectral sequence that one obtains by applying mod 2 homology to the Goodwillie tower which sends a spectrum X to the suspension spectrum of its 0th space X_0. This co…
Correction to ""Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology"
Nicholas J. Kuhn
Manfred Stelzer has pointed out that part of Corollary 4.5 of our paper "Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology" [Alg.…
Algebraic Topology (Hanoi, August 2004): The problem session
Carles Broto, Nguyen H V Hung, Nicholas J Kuhn +3
This article contains a collection of problems contributed during the course of the conference.
Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology
Nicholas J. Kuhn
We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space. What is most int…
A guide to telescopic functors
Nicholas J. Kuhn
In the mid 1980's, Pete Bousfield and I constructed certain p--local `telescopic' functors Phi_n from spaces to spectra, for each prime p and each positive integer n. These have st…
Goodwillie towers and chromatic homotopy: an overview
Nicholas J Kuhn
This paper is based on talks I gave in Nagoya and Kinosaki in August of 2003. I survey, from my own perspective, Goodwillie's work on towers associated to continuous functors betwe…
Mapping spaces and homology isomorphisms
Nicholas J. Kuhn
Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E_* be a generalized homology theory. We use Goodwillie calculus methods to…
Tate cohomology and periodic localization of polynomial functors
Nicholas J. Kuhn
In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Lo…
Localization of Andre-Quillen-Goodwillie towers, and the periodic homology of infinite loopspaces
Nicholas J. Kuhn
Let K(n) be the nth Morava K--theory at a prime p. This paper is a thorough study of questions like the following: to what extent does the K(n)--localization, or the K(n)--homology…
The McCord model for the tensor product of a space and a commutative ring spectrum
Nicholas J. Kuhn
This paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of…
Product and other fine structure in polynomial resolutions of mapping spaces
Stephen T. Ahearn, Nicholas J. Kuhn
Let Map_T(K,X) denote the mapping space of continuous based functions between two based spaces K and X. If K is a fixed finite complex, Greg Arone has recently given an explicit mo…