318 research outputs found
Stratifying derived categories of cochains on certain spaces
In recent years, Benson, Iyengar and Krause have developed a theory of
stratification for compactly generated triangulated categories with an action
of a graded commutative Noetherian ring. Stratification implies a
classification of localizing and thick subcategories in terms of subsets of the
prime ideal spectrum of the given ring. In this paper two stratification
results are presented: one for the derived category of a commutative
ring-spectrum with polynomial homotopy and another for the derived category of
cochains on certain spaces. We also give the stratification of cochains on a
space a topological content.Comment: 27 page
Exploring the reactivity of 2-trichloromethylbenzoxazoles for access to substituted benzoxazoles
The reactivity of 2-trichloromethylbenzoxazoles towards various nucleophiles, under metal free or iron-catalyzed conditions, for the synthesis of substituted benzoxazoles is described. These methods allow for selective substitution at either the 2- or 2’- position of the benzoxazoles using the same starting materials / reagents. This approach allows for the controlled synthesis of a variety of key derivatives from a single 2-trichloromethylbenzoxazole starting material
Brown representability for space-valued functors
In this paper we prove two theorems which resemble the classical
cohomological and homological Brown representability theorems. The main
difference is that our results classify small contravariant functors from
spaces to spaces up to weak equivalence of functors.
In more detail, we show that every small contravariant functor from spaces to
spaces which takes coproducts to products up to homotopy and takes homotopy
pushouts to homotopy pullbacks is naturally weekly equivalent to a
representable functor.
The second representability theorem states: every contravariant continuous
functor from the category of finite simplicial sets to simplicial sets taking
homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a
representable functor. This theorem may be considered as a contravariant analog
of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of
Mathematic
BV-structures on the homology of the framed long knot space
We introduce BV-algebra structures on the homology of the space of framed
long knots in in two ways. The first one is given in a similar
fashion to Chas-Sullivan's string topology. The second one is defined on the
Hochschild homology associated with a cyclic, multiplicative operad of graded
modules. The latter can be applied to Bousfield-Salvatore spectral sequence
converging to the homology of the space of framed long knots. Conjecturally
these two structures coincide with each other.Comment: 13 pages, 3 figures, to appear in Journal of Homotopy and Related
Structure
On the Whitehead spectrum of the circle
The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and
Williams shows that the homotopy groups in low degrees of the space of
homeomorphisms of a closed Riemannian manifold of negative sectional curvature
can be expressed as a functor of the fundamental group of the manifold. To
determine this functor, however, it remains to determine the homotopy groups of
the topological Whitehead spectrum of the circle. The cyclotomic trace of B
okstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an
expression for these homotopy groups in terms of the equivariant homotopy
groups of the homotopy fiber of the map from the topological Hochschild
T-spectrum of the sphere spectrum to that of the ring of integers induced by
the Hurewicz map. We evaluate the latter homotopy groups, and hence, the
homotopy groups of the topological Whitehead spectrum of the circle in low
degrees. The result extends earlier work by Anderson and Hsiang and by Igusa
and complements recent work by Grunewald, Klein, and Macko.Comment: 52 page
Empty spaces and the value of symbols: Estonia's 'war of monuments' from another angle
Taking as its point of departure the recent heightened discussion surrounding publicly sited monuments in Estonia, this article investigates the issue from the perspective of the country's eastern border city of Narva, focusing especially upon the restoration in 2000 of a 'Swedish Lion' monument to mark the 300th anniversary of Sweden's victory over Russia at the first Battle of Narva. This commemoration is characterised here as a successful local negotiation of a potentially divisive past, as are subsequent commemorations of the Russian conquest of Narva in 1704. A recent proposal to erect a statue of Peter the Great in the city, however, briefly threatened to open a new front in Estonia's ongoing 'war of monuments'. Through a discussion of these episodes, the article seeks to link the Narva case to broader conceptual issues of identity politics, nationalism and post-communist transition
Oxa-Michael-initiated cascade reactions of levoglucosenone
The reactions of aromatic aldehydes and levoglucosenone promoted by methoxide gives bridged α,β-unsaturated ketones, formed by a series of oxa-Michael-initiated cascade reactions in yields of up to 91% (14 examples). A complex series of equilibria operate during the reaction, and the formation of the bridged species is thermodynamically favored, except in the case of 5-methylfurfural and pyrrole-2-carboxaldehyde. This is the first report detailing this type of aldol/Michael cascade involving oxa-Michael initiation
The stable free rank of symmetry of products of spheres
A well known conjecture in the theory of transformation groups states that if
p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less
than or equal to k. We prove this assertion if p is large compared to the
dimension of the product of spheres. The argument builds on tame homotopy
theory for non simply connected spaces.Comment: 30 pages; improved exposition, some details adde
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