Whole body measurement systems

A system for measuring the volume and volume variations of a human body under zero gravity conditions is disclosed. An enclosed chamber having a defined volume and arranged for receiving a human body is provided with means for infrasonically varying the volume of the chamber. The changes in volume produce resultant changes in pressure, and under substantially isentropic conditions, an isentropic relationship permits a determination of gas volume which, in turn, when related to total chamber volume permits a determination of the body volume. By comparison techniques, volume changes of a human independent of gravity conditions can be determined

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Bounded homotopy theory and the KK-theory of weighted complexes

Given a bounding class $B$, we construct a bounded refinement $BK(-)$ of Quillen's $K$-theory functor from rings to spaces. $BK(-)$ is a functor from weighted rings to spaces, and is equipped with a comparison map $BK \to K$ induced by "forgetting control". In contrast to the situation with $B$-bounded cohomology, there is a functorial splitting $BK(-) \simeq K(-) \times BK^{rel}(-)$ where $BK^{rel}(-)$ is the homotopy fiber of the comparison map.Comment: 25 pages, 13 diagrams; comments welcom

B-Bounded cohomology and applications

A discrete group with word-length (G,L) is B-isocohomological for a bounding classes B if the comparison map from B-bounded cohomology to ordinary cohomology (with complex coefficients) is an isomorphism; it is strongly B-isocohomological if the same is true with arbitrary coefficients. In this paper we establish some basic conditions guaranteeing strong B-isocohomologicality. In particular, we show strong B-isocohomologicality for an $FP^{\infty}$ group G if all of the weighted G-sensitive Dehn functions are B-bounded. Such groups include all B-asynchronously combable groups; moreover, the class of such groups is closed under constructions arising from groups acting on an acyclic complex. We also provide examples where the comparison map fails to be injective, as well as surjective, and give an example of a solvable group with quadratic first Dehn function, but exponential second Dehn function. Finally, a relative theory of B-bounded cohomology of groups with respect to subgroups is introduced. Relative isocohomologicality is determined in terms of a new notion of relative Dehn functions and a relative $FP^\infty$ property for groups with respect to a collection of subgroups. Applications for computing B-bounded cohomology of groups are given in the context of relatively hyperbolic groups and developable complexes of groups.Comment: 50 pages. Accepted, IJA