This work provides a detailed exposition of a classical topic from a very recent viewpoint. We describe some foundational aspects of "Lawson homology" for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles.…
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
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 …
This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semiflow (with some mild compactness conditions) a homotopy type of a space, constructed to be invariant under perturbations…
Ordinal invariants in topology
by Kannan, V.
fromMemoirs of the American Mathematical Society
In this work we show that almost all useful ordinal invariants in topology studied until now (such as derived length of scattered spaces, sequential order of sequential spaces, etc.) can be brought under the single heading of what we call the order of a map. This helps us to per…
This memoir considers only the case of compact Menger-space-manifolds. With routine changes (open covers instead of epsilonics), the results are valid for non-compact Menger-space-manifolds. Also outlined are parts of proofs for the non-compact case that are substantially differ…
Studieboek voor het hoger onderwijs.
"Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth…
This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homolog…