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- Steven R Costenoble, Stefan Waner
- 2009

We develop machinery enabling us to show that suitable G-spaces, including the equivariant version of BF , are equivariant infinite loop spaces. This involves a "recognition principle" for systems of spaces which behave formally like the system of fixed sets of a G-space; that is, we give a necessary and sufficient condition for such a system to be… (More)

- Steven R Costenoble, Stefan Waner
- 1996

We generalize the results of CW92b] to compact Lie groups. Using a suitable ordinary equivariant homology and coho-mology, we deene equivariant Poincarr e complexes with the properties that (1) every compact G-manifold is an equivariant Poincarr e complex, (2) every nite equivariant Poincarr e complex (with some mild additional hypotheses) has an… (More)

Biological systems routinely solve problems involving pattern recognition and feature extraction. Such problems do not appear to admit similarly routine algorithmic solutions; the power of biological systems in this regard apparently arises from nonalgorithmic dynamics. It is our intention to explore, and to develop principles of, functional characteristics… (More)

- Steven R Costenoble, Stefan Waner
- 2007

Bibliography 135 iii Introduction Poincaré duality lies at the heart of the homological study of manifolds. In the presence of the action of a group, it is well-known that Poincaré duality fails to hold in ordinary, integer-graded (Bredon-Illman) equivariant homology. (See [3] and [21] for the construction of these homology theories; see [17] and [30] for… (More)

We give a long overdue theory of orientations of G-vector bundles, topological G-bundles, and spherical G-fibrations, where G is a compact Lie group. The notion of equivariant orientability is clear and unambiguous, but it is surprisingly difficult to obtain a satisfactory notion of an equivariant orientation such that every orientable G-vector bundle… (More)

- Steven R Costenoble, Stefan Waner
- 2008

Bibliography 109 iii Introduction Poincaré duality lies at the heart of the homological theory of manifolds. In the presence of the action of a group it is well-known that Poincaré duality fails to hold in ordinary, integer-graded (Bredon-Illman) equivariant homology. (See [Bre67] and [Ill75] for the construction of these homology theories; see [DR88] and… (More)