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- S R Costenoble, J P May, S Waner
- 2002

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)

We generalize the results of [CW92b] to compact Lie groups. Using a suitable ordinary equivariant homology and cohomology, we define equivariant Poincaré complexes with the properties that (1) every compact G-manifold is an equivariant Poincaré complex, (2) every finite equivariant Poincaré complex (with some mild additional hypotheses) has an equivariant… (More)

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)

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)

- H M Hastings, S Waner
- Bio Systems
- 1985

Biological systems frequently need to solve many computationally hard decision and optimization problems. The solution of these problems by digital computers as presently understood requires exponentially large energy dissipation. This severely restricts the ability of digital computers to attack such problems. We shall show that only polynomial dissipation… (More)

- Stefan Waner, Yihren Wu
- Inf. Comput.
- 1987

- H M Hastings, S Waner
- Bio Systems
- 1985

We propose an automata-theoretical framework for structured hierarchical control, in terms of rules and meta-rules, for sequences of moves on a graph. This leads to a notion of a "universal" hierarchically structured automaton mu which can move on a given graph in such a way as to emulate any automaton which moves on that graph in response to inputs. This… (More)

- Harold M. Hastings, Stefan Waner
- SIGART Newsletter
- 1986

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)

- I. Kadar, Stefan Waner, Yihren Wu, Harold M. Hastings
- Neural Networks
- 1988