20 research outputs found
Embeddings from the point of view of immersion theory: Part II
Let M and N be smooth manifolds. For an open V of M let emb(V,N) be the space
of embeddings from V to N. By results of Goodwillie and Goodwillie-Klein, the
cofunctor V |--> emb(V,N) is analytic if dim(N)-dim(M) > 2. We deduce that its
Taylor series converges to it. For details about the Taylor series, see Part I.Comment: 16 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol3/paper4.abs.htm
Calculus III: Taylor Series
We study functors from spaces to spaces or spectra that preserve weak
homotopy equivalences. For each such functor we construct a universal
n-excisive approximation, which may be thought of as its n-excisive part.
Homogeneous functors, meaning n-excisive functors with trivial (n-1)-excisive
part, can be classified: they correspond to symmetric functors of n variables
that are reduced and 1-excisive in each variable. We discuss some important
examples, including the identity functor and Waldhausen's algebraic K-theory.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper19.abs.htm
A stable range description of the space of link maps
We study the space of link maps, which are smooth maps from the disjoint
union of manifolds P and Q to a manifold N such that the images of P and Q are
disjoint. We give a range of dimensions, interpreted as the connectivity of a
certain map, in which the cobordism class of the "linking manifold" is enough
to distinguish the homotopy class of one link map from another.Comment: 10 page