Integration of simplicial forms and Deligne cohomology

We present two approaches to constructing an integration map for smooth Deligne cohomology. The first is defined in the simplicial model, where a class in Deligne cohomology is represented by a simplicial form, and the second in a related but more combinatorial model.Comment: 28 pages, section on products adde

Cobordism obstructions to independent vector fields

We define an invariant for the existence of r pointwise linearly independent sections in the tangent bundle of a closed manifold. For low values of r, explicit computations of the homotopy groups of certain Thom spectra combined with classical obstruction theory identifies this invariant as the top obstruction to the existence of the desired sections. In particular, this shows that the top obstruction is an invariant of the underlying manifold in these cases, which is not true in general. The invariant is related to cobordism theory and this gives rise to an identification of the invariant in terms of well-known invariants. As a corollary to the computations, we can also compute low-dimensional homotopy groups of the Thom spectra studied by Galatius, Tillmann, Madsen, and Weiss.Comment: 46 page

Gerbes, simplicial forms and invariants for families of foliated bundles

The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to `characteristic gerbes' associated to families of bundles and connections. In turn this gives invariants for families of foliated bundles. A special case is the Quillen line bundle associated to families of flat SU(2)-bundlesComment: 28 page

Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Defining Responses to Therapy and Study Outcomes in Clinical Trials of Invasive Fungal Diseases: Mycoses Study Group and European Organization for Research and Treatment of Cancer Consensus Criteria

Invasive fungal diseases (IFDs) have become major causes of morbidity and mortality among highly immunocompromised patients. Authoritative consensus criteria to diagnose IFD have been useful in establishing eligibility criteria for antifungal trials. There is an important need for generation of consensus definitions of outcomes of IFD that will form a standard for evaluating treatment success and failure in clinical trials. Therefore, an expert international panel consisting of the Mycoses Study Group and the European Organization for Research and Treatment of Cancer was convened to propose guidelines for assessing treatment responses in clinical trials of IFDs and for defining study outcomes. Major fungal diseases that are discussed include invasive disease due to Candida species, Aspergillus species and other molds, Cryptococcus neoformans, Histoplasma capsulatum, and Coccidioides immitis. We also discuss potential pitfalls in assessing outcome, such as conflicting clinical, radiological, and/or mycological data and gaps in knowledg