1.
The mathematical work of Douglas C. Ravenel - Hopkins, Michael J.
This is a transcription of my talk on the work of Doug Ravenel. While it was intended as a one-time performance,
the organizers felt it would be a good idea to have some representation appear as part of the conference
proceedings. Don Davis went to the great trouble of transcribing the lecture from a video, and he sent it to me.
After reading it I agreed to have it included in these proceedings. Even though the text is ungrammatical,
repetitious and meandering (apparently that's how I talk), it feels to me as if it conveys something about how
the world of algebraic topology has felt...
2.
W. Stephen Wilson's contributions to homotopy theory - Bendersky, Martin
This paper is a survey of Steve's work on BP and periodic cohomology theories. It was presented as a talk given
in March 2007 at a conference celebrating Steve's 60th birthday.
5.
Extended powers and Steenrod operations in algebraic geometry - Bisson, Terrence; Tsemo, Aristide
Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato
conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper
is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology
theories whose formal group law has order two. We adapt the methods used by Bisson-Joyal in studying Steenrod and
Dyer-Lashof operations in unoriented cobordism and mod 2 cohomology.
6.
The ring spectrum $P(n)$ for the prime 2 - Boardman, J. Michael
This paper is a companion to the Boardman-Wilson paper on the ring spectrum $P(n)$. When the prime is 2, this
spectrum is not commutative, which introduces several complications. Here, we supply the necessary details
of the relevant Hopf algebroids and Hopf ring for this case.
7.
Explicit fibrant replacement for discrete G-spectra - Davis, Daniel G.
If $C$ is the model category of simplicial presheaves on a site with enough points, with fibrations equal to the
global fibrations, then it is well-known that the fibrant objects are, in general, mysterious. Thus, it is not surprising
that, when $G$ is a profinite group, the fibrant objects in the model category of discrete $G$-spectra are also difficult
to get a handle on. However, with simplicial presheaves, it is possible to construct an explicit fibrant model for an
object in $C$, under certain finiteness conditions. Similarly, in this paper, we show that if $G$ has finite virtual
cohomological dimension and $X$ is a discrete...
8.
Nonimmersions of $RP^n$ implied by tmf, revisited - Davis, Donald M.; Mahowald, Mark
In a 2002 paper, the authors and Bruner used the new spectrum tmf to obtain some new nonimmersions of real
projective spaces. In this note, we complete/correct two oversights in that paper.
9.
The BP-theory of 2-fold products of real projective spaces - González, Jesús; Wilson, W. Stephen
We study the Brown-Peterson (co)homology of a product of two real projective spaces via the Landweber short exact
sequence. The image of the tensor product is well understood. Our contribution is to understand those elements
not in the tensor product and to show how they behave under maps. The results are partially extended to the case
where one of the factors is replaced by a $2^e$-torsion lens space.
13.
A guide to telescopic functors - Kuhn, Nicholas J.
In the mid 1980s, Pete Bousfield and I constructed certain $p$-local `telescopic' functors $Φ_n$ from spaces to spectra, for each
prime $p$, and each $n ≥ 1$. They are constructed using the full strength of the Nilpotence and Periodicity Theorems of
Devanitz-Hopkins-Smith, and have some striking properties that relate the chromatic approach to homotopy theory to
infinite loopspace theory.
¶ Recently there have been a variety of new uses of these functors, suggesting that they have a central role to play in
calculations of periodic phenomena. Here I offer a guide to their construction, characterization, application, and
computation.
14.
An algebraic generalization of image $J$ - Nakai, Hirofumi
As is well known, the image of the $J$-homomorphism in the stable homotopy groups of spheres is described in terms
of the first line of the Adams-Novikov $E_2$-term. In this paper we consider an algebraic analogue of the image of $J$
using the spectrum $T(m)_(j)$ defined by Ravenel and determine the Adams-Novikov first line for small values of $j$.
16.
A universal property for $Sp(2)$ at the prime $3$ - Grbić, Jelena; Theriault, Stephen
We study a universal property of $Sp(2)$ in the category of $3$-local homotopy associative, homotopy commutative
$H$-spaces. We show that while $Sp(2)$ fails to be universal in the full category, there is a subcategory in which
it is universal for its $7$-skeleton.
17.
Umkehr maps - Cohen, Ralph L.; Klein, John R.
In this note, we study umkehr maps in generalized (co)homology theories arising from the Pontrjagin-Thom construction,
from integrating along fibers, pushforward homomorphisms, and other similar constructions. We consider the basic
properties of these constructions and develop axioms which any umkehr homomorphism must satisfy. We use a
version of Brown representability to show that these axioms completely characterize these homomorphisms, and a
resulting uniqueness theorem follows. Finally, motivated by constructions in string topology, we extend this axiomatic
treatment of umkehr homomorphisms to a fiberwise setting.
18.
Homotopy theory of presheaves of Γ-spaces - Bergsaker, Håkon Schad
We consider the category of presheaves of Γ-spaces, or equivalently, of Γ-objects in simplicial presheaves. Our main
result is the construction of stable model structures on this category parametrised by local model structures on
simplicial presheaves. If a local model structure on simplicial presheaves is monoidal, then the corresponding
stable model structure on presheaves of Γ-spaces is monoidal and satisfies the monoid axiom. This allows us to
lift the stable model structures to categories of algebras and modules over a monoid.
19.
Homotopy nilpotency in localized $SU(n)$ - Kishimoto, Daisuke
We determine the homotopy nilpotency of $p$-localized $SU(n)$ when $p$ is a quasi-regular prime in the sense of
M. Mimura and H. Toda, "Cohomology operations and homotopy of compact Lie groups I," Topology 9
(1970), 317–336. As a consequence, we see that it is not a monotonic decreasing function in $p$.
20.
Flat cyclic Fréchet modules, amenable Fréchet algebras, and approximate identities - Pirkovskii, A.Yu.
Let A be a locally $m$-convex Fréchet algebra. We give a necessary and sufficient condition for a cyclic Fréchet
$A-$module $X=A+/I$ to be strictly flat, generalizing thereby a criterion of Helemskii and Sheinberg. To this end, we
introduce a notion of "locally bounded approximate identity" (a locally b.a.i. for short), and we show that $X$ is strictly
flat if and only if the ideal I has a right locally b.a.i. Next we apply this result to amenable algebras and show that a
locally $m$-convex Fréchet algebra $A$ is amenable if and only if $A$ is isomorphic to a reduced inverse limit of
amenable Banach algebras....
1.
