Related papers: Pansu pullback and spectral complexes

We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group $G$ to smooth maps into a homogeneous space $M=G/H$, and determine the global monodromy obstruction to reconstructing such maps from…

We upgrade the classical operation of \textit{isomonodromic deformations} along a path $\gamma$ to a functor $\mathbb{P}_{\gamma}$ between categories of flat connections with logarithmic singularities along a divisor $D$, which itself…

We define a new version of $\mathbb A^1$-homology, called cellular $\mathbb A^1$-homology, for smooth schemes over a field that admit an increasing filtration by open subschemes with cohomologically trivial closed strata. We provide several…

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

We study here compact manifolds with positive scalar curvature metrics. We use the relative Yamabe invariant from math.DG/0008138 to define the conformal cobordism relation on the category of such manifolds. We prove that corresponding…

These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in…

In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \cite{Crai} that such connections up to homotopy can be used to compute the classical Chern…

We improve the main results in the paper from the title using a recent refinement of Bronshtein's theorem due to Colombini, Orr\'u, and Pernazza. They are then in general best possible both in the hypothesis and in the outcome. As a…

In the 1970s and again in the 1990s, Gromov gave a number of theorems and conjectures motivated by the notion that the real homotopy theory of compact manifolds and simplicial complexes influences the geometry of maps between them. The main…

We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.

Let $p$ be a prime number, and let $A$ be a ring in which $p$ is nilpotent. In this paper, we consider the maps $$K_{q+1}(A[x]/(x^m), (x))\to K_{q+1}(A[x]/(x^{mn}), (x)),$$induced by the ring homomorphism $A[x]/(x^{m})\to A[x]/(x^{mn})$,…

We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…

The image of the branch set of a PL branched cover between PL $n$-manifolds is a simplicial $(n-2)$-complex. We demonstrate that the reverse implication also holds: an open and discrete map $f \colon \mathbb{S}^n \to \mathbb{S}^n$ with the…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…

We define and study an analogue of the Baum-Connes assembly map for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. Our starting point is the deformation picture of the…

We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective…

We prove that the group of automorphisms of the Lie algebra $\Der_K (P_n)$ of derivations of a polynomial algebra $P_n=K[x_1,..., x_n]$ over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…

The motivation for this paper stems \cite{CR} from the need to construct explicit isomorphisms of (possibly nontrivial) principal $G$-bundles on the space of loops or, more generally, of paths in some manifold $M$, over which I consider a…