Deformations of topological spaces predicted by E-theory

Marius Dădărlat and Terry A. Loring
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Marius Dădărlat: University of Maryland, Department of Mathematics
Terry A. Loring: University of New Mexico, Department of Mathematics and Statistics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 316-327 from Springer

Abstract: Abstract LetX be a locally compact space. By a deformation of X we mean a continuous field {A t | t ∈ [0, 1]} of C*-algebras with A 0 ≅ C 0(X), $$\left\{ {{{A}_{t}}|t \in \left( {0,1]} \right.} \right\} \cong B \times \left( {0,1]} \right.$$ and for a fixed C*-algebra B. Replacing C 0(X by another. C*-algebra A, we generalize this to a deformation of one C*-algebra to another. This is a basic interpretation of deformation—it reflects only the topology of X and omits more general fields of algebras—but is an important one. This importance is seen in the relation to E-theory and the examples [3, 9, 13, 14] that have arisen.

Keywords: Topological Space; Compact Space; Homotopy Class; Klein Bottle; Orientable Manifold (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-1-4612-0255-4_31

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