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We develop a general theory of extrapolation spaces, a complement to the familiar theory of interpolation spaces. Our results allow us to extend the classical extrapolation theorem of Yano to scales of Banach spaces. We give applications to classical and modern analysis includin…
The principal aim of this research is to establish certain formulas for the homology classes represented by the self-intersection loci of an immersed submanifold. This paper provides a generalization of a formula for higher order intersection multiplicities.
This memoir contains a careful, detailed proof of the multiple disjunction lemma for smooth concordance embeddings of codimension [greater than or equal to] 3. A great deal of the paper addresses the construction and derivation of properties of the algebraic stratification of th…
This paper deals with the two broad questions of how 3-manifold groups imbed in one another and how such imbeddings relate to any corresponding [lowercase Greek]Pi₁-injective maps. In particular, we are interested in 1) determining which 3-manifold groups are no cohopfian, that …
Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on…
The author considers the set [italic]G[italic subscript]n[italic superscript]t([italic]M) (where [italic]M is a manifold) of embeddings of [italic]S[italic superscript]n × [italic]M in [italic]S[italic superscript]n+[italic superscript]2 × [italic]M, homotopic (relative to the b…
The embeddability and structure of all locally compact one-to-one continuous metric (equivalently, Hausdorff) images of the real line are studied. The structure of such spaces is utilized to obtain, for example, necessary and sufficient conditions that they be embeddable in the …
![[Beta]-homotopy equivalences have [alpha]-cross sections](https://covers.openlibrary.org/b/isbn/0821822748-M.jpg?default=false)
The purpose of this paper is to study the following problem: When is there a locally flat embedding g: N[superscript]n [right arrow] M[superscript]m such that pg is [lowercase Greek]Alpha-close to h? This problem is intimately related to the problem of approximating topological …