1,541,603 research outputs found

### Amplifier enhances ring-down spectroscopy

In recent years, investigators have adapted the principles of ringdown spectroscopy (see sidebar, facing page) to fiber optic configurations by placing high reflectors on each end of a fiber and observing the ringdown time of an injected pulse. But a major drawback is the difficulty of creating a low-loss, high-Q resonator in an optical fiber

### Function spectra and continuous G-spectra

Let G be a profinite group, {X_alpha}_alpha a cofiltered diagram of discrete
G-spectra, and Z a spectrum with trivial G-action. We show how to define the
homotopy fixed point spectrum F(Z, holim_alpha X_alpha)^{hG} and that when G
has finite virtual cohomological dimension (vcd), it is equivalent to F(Z,
holim_alpha (X_alpha)^{hG}). With these tools, we show that the K(n)-local
Spanier-Whitehead dual is always a homotopy fixed point spectrum, a well-known
Adams-type spectral sequence is actually a descent spectral sequence, and, for
a sufficiently nice k-local profinite G-Galois extension E, with K a closed
normal subgroup of G, the equivalence (E^{h_kK})^{h_kG/K} \simeq E^{h_kG} (due
to Behrens and the author), where (-)^{h_k(-)} denotes k-local homotopy fixed
points, can be upgraded to an equivalence that just uses ordinary (non-local)
homotopy fixed points, when G/K has finite vcd.Comment: submitted for publicatio

### Symmetric spectra

The long hunt for a symmetric monoidal category of spectra finally ended in
success with the simultaneous discovery of the third author's discovery of
symmetric spectra and the Elmendorf-Kriz-Mandell-May category of S-modules. In
this paper we define and study the model category of symmetric spectra, based
on simplicial sets and topological spaces. We prove that the category of
symmetric spectra is closed symmetric monoidal and that the symmetric monoidal
structure is compatible with the model structure. We prove that the model
category of symmetric spectra is Quillen equivalent to Bousfield and
Friedlander's category of spectra. We show that the monoidal axiom holds, so
that we get model categories of ring spectra and modules over a given ring
spectrum.Comment: 77 pages. This version corrects some errors in the section on
topological symmetric spectr

### Spectra and symmetric spectra in general model categories

(This is an updated version; following an idea of Voevodsky, we have
strengthened our results so all of them apply to one form of motivic homotopy
theory).
We give two general constructions for the passage from unstable to stable
homotopy that apply to the known example of topological spaces, but also to new
situations, such as motivic homotopy theory of schemes. One is based on the
standard notion of spectra originated by Boardman. Its input is a well-behaved
model category C and an endofunctor G, generalizing the suspension. Its output
is a model category on which G is a Quillen equivalence. Under strong
hypotheses the weak equivalences in this model structure are the appropriate
analogue of stable homotopy isomorphisms.
The second construction is based on symmetric spectra, and is of value only
when C has some monoidal structure that G preserves. In this case, ordinary
spectra generally will not have monoidal structure, but symmetric spectra will.
Our abstract approach makes constructing the stable model category of symmetric
spectra straightforward. We study properties of these stabilizations; most
importantly, we show that the two different stabilizations are Quillen
equivalent under some hypotheses (that also hold in the motivic example).Comment: 45 page

### Diagram spaces, diagram spectra, and spectra of units

This article compares the infinite loop spaces associated to symmetric
spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of
structured spectra has a corresponding category of structured spaces that
receives the infinite loop space functor \Omega^\infty. We prove that these
models for spaces are Quillen equivalent and that the infinite loop space
functors \Omega^\infty agree. This comparison is then used to show that two
different constructions of the spectrum of units gl_1 R of a commutative ring
spectrum R agree.Comment: 62 pages. The definition of the functor \mathbb{Q} is changed.
Sections 8, 9, 17 and 18 contain revisions and/or new materia

### Mad Spectra

The mad spectrum is the set of all cardinalities of infinite maximal almost
disjoint families on omega. We treat the problem to characterize those sets A
which, in some forcing extension of the universe, can be the mad spectrum. We
solve this problem to some extent. What remains open is the possible values of
min(A) and max(A)

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