What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and from Lie groups to higher connected covers of Lie groups by smooth ∞-groups, i.e., by smooth groupal A∞spaces. Namely, we realize differential characteristic classes as morphisms from ∞-groupoids of smooth principal ∞-bundles with connections to ∞-groupoids of higher U (1)-gerbes with connections. This allows us to study the homotopy fibers of the differential characteristic maps thus obtained and to show how these describe differential obstruction problems. This applies in particular to the higher twisted differential spin structures called twisted differential string structures and twisted differential fivebrane structures.

We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by the second author in [19].Keywords and general notation. We assume that the reader is familiar with the notion and main properties of differential graded Lie algebras and L ∞ -algebras (we refer to [7,9,11,14,15,18] as introduction of such structures); however the basic definitions

We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the “FDA”-language used in the\ud supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting “extended (super-)spacetimes”\ud formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the “old brane scan”) but also the branes with tensor multiplet worldvolume fields, notably\ud the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the “M-theory super-Lie algebra”. We also observe that in this formulation there is a\ud simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZWtype\ud σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology

The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details -in particular the global moduli / instanton / magnetic charge structure -have remained elusive. Here we deduce from anomaly cancellation a natural candidate for the holographic dual of this nonabelian 2-form field, under AdS7/CFT6 duality. We find this way a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

Patients with amyotrophic lateral sclerosis (ALS) need a care programme as the disease progresses. We used telemedicine-assisted integrated care (TAIC) in 40 patients with ALS, for a mean duration of 8.6 months (range 1-12). A nurse-tutor played the key role, supported by respiratory physicians, neurologists and psychologists. Each patient used a portable pulse oximeter during the daily telephone contacts to assess clinical/oxygen variations. Patients also completed a satisfaction questionnaire. During the study period, each patient used TAIC at least five times per month. There were 1907 scheduled telephone calls (86% of the total) and 317 unscheduled calls. Of the unscheduled calls, 84% were managed by the nurse-tutor and only 16% of them required specialist intervention. The most common item was the ALS clinical interview (58%), followed by the description of acute symptoms, cough ability and oxygenation. TAIC staff recommended 4 out of 12 emergency hospital admissions (33%) and 77% of the other hospitalizations. Patients and caregivers were extremely satisfied (79%) with the nurse assistance provided and the patients' confidence in handling their disease improved in 71% of the cases. TAIC provides a nurse-centred, home-monitoring programme that can be a useful way of following up ALS patients.

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Abstract. The proper action functional of (4k + 3)-dimensional U (1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k + 2) differential cohomology. We first refine this statement from the moduli space to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String c -2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric pre-quantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum U (1)-k-bundle (equivalently: a U (1)-(k − 1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, appearing as line bundles with connection on the smooth higher moduli stacks of field configurations.

To any manifold equipped with a higher degree closed form, one can associate an L ∞ -algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L ∞ -algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produce analogues of the (higher) Lie algebras of sections of the Atiyah Lie algebroid and of the Courant Lie 2-algebroid. We also exhibit the L ∞ -cocycle that realizes the L ∞ -algebra of local observables as a KirillovKostant-Souriau-type L ∞ -extension of the Hamiltonian vector fields. When restricted along a Lie algebra action, this yields Heisenberg-like L ∞ -algebras such as the string Lie 2-algebra of a semisimple Lie algebra.