Equivariant s-cobordism theorems

Araki, Shôrô; Kawakubo, Katsuo

doi:10.2969/jmsj/04020349

Cited by 10 publications

(9 citation statements)

References 13 publications

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“…Finally, the group (W H) * α is an extension of (W H) α by π 1 (X H α ). As expected, the equivariant Whitehead group appears in the equivariant s-cobordism theorem in [83] and in [4].…”

Section: Equivariant and Stratified Situationssupporting

confidence: 79%

K-Theory and Geometric Topology

Rosenberg

2005

Handbook of K-Theory

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Historically, one of the earliest motivations for the development of K-theory was the need to put on a firm algebraic foundation a number of invariants or obstructions that appear in topology. The primary purpose of this chapter is to examine many of these K-theoretic invariants, not from a historical point of view, but rather a posteriori, now that K-theory is a mature subject. There are two reasons why this may be a useful exercise. First, it may help to show K-theorists brought up in the "algebraic school" how their subject is related to topology. And secondly, clarifying the relationship between Ktheory and topology may help topologists to extract from the wide body of K-theoretic literature the things they need to know to solve geometric problems. For purposes of this article, "geometric topology" will mean the study of the topology of manifolds and manifold-like spaces, of simplicial and CWcomplexes, and of automorphisms of such objects. As such, it is a vast subject, and so it will be impossible to survey everything that might relate this subject to K-theory. I instead hope to hit enough of the interesting areas to give the reader a bit of a feel for the subject, and the desire to go off and explore more of the literature. Unless stated otherwise, all topological spaces will be assumed to be Hausdorff and compactly generated. (A Hausdorff space X is compactly generated if a subset C is closed if and only if C ∩K is closed, or equivalently, compact, for all compact subsets K of X. Sometimes compactly generated spaces are called k-spaces. The k stands both for the German Kompakt and for Kelley, who pointed out the advantages of these spaces.) This eliminates certain pathologies that cause trouble for the foundations of homotopy theory. "Map" will always mean "continuous map." A map f : X → Y is called a weak equivalence if its image meets every path component of Y and if f * : π n (X, x) → π n (Y, f (x)) is an isomorphism for every x ∈ X.

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Section: Equivariant and Stratified Situationssupporting

confidence: 79%

K-Theory and Geometric Topology

Rosenberg

2005

Handbook of K-Theory

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“…In order to circumvent these difficulties, one usually works with gap hypotheses of the form that each singular stratum which is properly contained in the closure of another singular stratum F must have a large enough codimension in F (cf. [1]) or one formulates the s-cobordism theorem in an isovariant context, see e.g. [17], Theorem 4.42.…”

Section: Equivariant Bordism Theoremmentioning

confidence: 99%

Positive scalar curvature with symmetry

Hanke¹

2008

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension-2 surgery technique which removes singular strata from fixed point free S 1 -manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following theorem: Each closed fixed point free S 1 -manifold of dimension at least 6 whose isotropy groups have odd order and whose union of maximal orbits is simply connected and not spin, carries an S 1 -invariant metric of positive scalar curvature.

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“…Agar, an unbranched polysaccharide, is a hydrophilic colloid extracted from the family of seaweeds (Rhodophycae) having the structure of 1,4-linked-3,6-anhydro-α-Lgalactopyranose 16 . One of the most important properties of agar is its ability to form reversible gels even at low concentration simply by cooling its hot aqueous solutions.…”

Section: Introductionmentioning

confidence: 99%

Preparation and Characterization of Chitosan/Agar Blended Films: Part 1. Chemical Structure and Morphology

El-Hefian

Nasef

Yahaya

2011

Journal of Chemistry

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Chitosan/agar (CS/AG) films were prepared by blending different proportions of chitosan and agar (considering chitosan as the main component) in solution forms. The chemical structure and the morphology of the obtained blended films were investigated using Fourier transform infrared (FTIR) and field emission scanning electron microscope (FESEM). It was revealed that chitosan and agar form a highly compatible blend and their films displayed homogenous and smooth surface properties compared to the individual pure components.

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Equivariant s-cobordism theorems

Cited by 10 publications

References 13 publications

K-Theory and Geometric Topology

K-Theory and Geometric Topology

Positive scalar curvature with symmetry

Preparation and Characterization of Chitosan/Agar Blended Films: Part 1. Chemical Structure and Morphology

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