Stefan Waner

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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)
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)
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)