13,513 research outputs found
Poincare submersions
We prove two kinds of fibering theorems for maps X --> P, where X and P are
Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue
of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-2.abs.html Version 5:
Statement of Theorem B corrected, see footnote p2
Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces
We prove that intersections and unions of independent random sets in finite
spaces achieve a form of Lipschitz continuity. More precisely, given the
distribution of a random set , the function mapping any random set
distribution to the distribution of its intersection (under independence
assumption) with is Lipschitz continuous with unit Lipschitz constant if
the space of random set distributions is endowed with a metric defined as the
norm distance between inclusion functionals also known as commonalities.
Moreover, the function mapping any random set distribution to the distribution
of its union (under independence assumption) with is Lipschitz continuous
with unit Lipschitz constant if the space of random set distributions is
endowed with a metric defined as the norm distance between hitting
functionals also known as plausibilities.
Using the epistemic random set interpretation of belief functions, we also
discuss the ability of these distances to yield conflict measures. All the
proofs in this paper are derived in the framework of Dempster-Shafer belief
functions. Let alone the discussion on conflict measures, it is straightforward
to transcribe the proofs into the general (non necessarily epistemic) random
set terminology
The Dualizing Spectrum, II
To an inclusion topological groups H->G, we associate a naive G-spectrum. The
special case when H=G gives the dualizing spectrum D_G introduced by the author
in the first paper of this series. The main application will be to give a
purely homotopy theoretic construction of Poincare embeddings in stable
codimension.Comment: Fixed an array of typo
On the homotopy invariance of configuration spaces
For a closed PL manifold M, we consider the configuration space F(M,k) of
ordered k-tuples of distinct points in M. We show that a suitable iterated
suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we
require depends on three parameters: the number of points k, the dimension of M
and the connectivity of M. Our proof uses a mixture of Poincare embedding
theory and fiberwise algebraic topology.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-35.abs.htm
A chain rule in the calculus of homotopy functors
We formulate and prove a chain rule for the derivative, in the sense of
Goodwillie, of compositions of weak homotopy functors from simplicial sets to
simplicial sets. The derivative spectrum dF(X) of such a functor F at a
simplicial set X can be equipped with a right action by the loop group of its
domain X, and a free left action by the loop group of its codomain Y = F(X).
The derivative spectrum d(E o F)(X)$ of a composite of such functors is then
stably equivalent to the balanced smash product of the derivatives dE(Y) and
dF(X), with respect to the two actions of the loop group of Y. As an
application we provide a non-manifold computation of the derivative of the
functor F(X) = Q(Map(K, X)_+).Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol6/paper25.abs.htm
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