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

Truth and Probability

Contains two other essays as well: Further Considerations & Last Papers: Probability and Partial Belief.

Growing a Rural Economy with an Entrepreneurial Community College

Community/Rural/Urban Development,

Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects

We present a detailed and systematic analysis of the nonperturbative, nonequilibrium dynamics of a quantum field in the reheating phase of inflatonary cosmology, including full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field. We use the O(N) field theory with unbroken symmetry in a spatially flat FRW universe to study the dynamics of the inflaton in the post-inflaton, preheating stage. Oscillations of the inflaton's zero mode induce parametric amplification of quantum fluctuations, resulting in a rapid transfer of energy to the inhomogeneous modes of the inflaton field. We adopt the coupled nonperturbative equations for the mean field and variance derived in a preceding paper [gr-qc/9706001] by means of a two-particle-irreducible (2PI), closed-time-path (CTP) effective action for curved spacetime while specialized to leading order in the 1/N expansion. Adiabatic regularization is employed. The renormalized dynamical equations are evolved numerically from initial data which are generic to the end state of slow roll in many inflatonary cosmological scenarios. The initial conditions consist of a large-amplitude, quasiclassical, oscillating mean field, and a variance given by the de Sitter-invariant vacuum. We find that for sufficiently large initial mean-field amplitudes in this model, the parametric resonance effect alone (in a collisionless approximation) is not an efficient means to "preheat" the quantum field. For small initial mean-field amplitude, damping of the mean field via parametric amplification of quantum fluctuations is seen to occur. Our results indicate that the self-consistent dynamics of spacetime plays an important role in determining the physics of the post-inflatonary Universe.Comment: 53 pages, 19 figures. The bound on the initial inflaton amplitude has been strengthened (the qualitative results of the paper are unchanged

Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture

By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy-bound property and nilpotent periodicity property, satisfy the $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\ell^1$-algebra of any discrete group.Comment: 32 pages, 2 figures; added an appendix also by C. Ogl

In the Sweat Box: A Historical Perspective on the Detention of Material Witnesses

After the September 11 terrorist attacks, the Justice Department detained scores of allegedly suspicious persons under a federal material witness statute--a tactic that provoked a great deal of controversy. Most critics assume that the abuse of material witness laws is a new development. Yet, rather than being transformed by the War on Terror, the detention of material witnesses is a coercive strategy that police officers across the nation have used since the nineteenth century to build cases against suspects. Fears of extraordinary violence or social breakdown played at most an indirect role in its advent and growth. Rather, it has long been used to obtain prosecution evidence in ordinary cases of murder, robbery, prostitution, and other street crimes. Historically, no stark divide between the innocent witness and the suspected criminal existed in the minds of the police. Indeed, material witness detention contributed to the rise of incommunicado interrogation and numbered among the tactics identified in the Wickersham Commission\u27s expose of the third degree in 1931. This Essay demonstrates that the story of material witness detention is one of stasis, not of change. For more than a century, the field practices of police and magistrates have been unresponsive to reforms in statutory and constitutional law or to sporadic public pressure on behalf of detainees deemed to have knowledge of a crime. In telling such a story, this Essay seeks, not to defend the Justice Department, but to suggest that intense scholarly focus on September 11 as a watershed in the history of criminal procedure obscures ways in which the gradual consolidation of governmental power over more than a century has fostered an increasingly coercive and secretive relationship between the individual and the police

Rapid turnover of hyphae of mycorrhizal fungi determined by AMS microanalysis of C-14

Processes in the soil remain among the least well-characterized components of the carbon cycle. Arbuscular mycorrhizal (AM) fungi are ubiquitous root symbionts in many terrestrial ecosystems and account for a large fraction of photosynthate in a wide range of ecosystems; they therefore play a key role in the terrestrial carbon cycle. A large part of the fungal mycelium is outside the root ( the extraradical mycelium, ERM) and, because of the dispersed growth pattern and the small diameter of the hyphae (<5 micrometers), exceptionally difficult to study quantitatively. Critically, the longevity of these. ne hyphae has never been measured, although it is assumed to be short. To quantify carbon turnover in these hyphae, we exposed mycorrhizal plants to fossil ("carbon-14 - dead") carbon dioxide and collected samples of ERM hyphae ( up to 116 micrograms) over the following 29 days. Analyses of their carbon-14 content by accelerator mass spectrometry (AMS) showed that most ERM hyphae of AM fungi live, on average, 5 to 6 days. This high turnover rate reveals a large and rapid mycorrhizal pathway of carbon in the soil carbon cycle

Chiral Symmetry and the Parity-Violating NNπNN\pi Yukawa Coupling

We construct the complete SU(2) parity-violating (PV) $\pi, N, \Delta$ interaction Lagrangian with one derivative, and calculate the chiral corrections to the PV Yukawa $NN\pi$ coupling constant $h_\pi$ through ${\cal O}(1/\Lambda_\chi^3)$ in the leading order of heavy baryon expansion. We discuss the relationship between the renormalized \hpi, the measured value of \hpi, and the corresponding quantity calculated microscopically from the Standard Model four-quark PV interaction.Comment: RevTex, 26 pages + 5 PS figure