Related papers: Mapping the surgery exact sequence for topological…

We generalize a bi-Lipschitz extension result of David and Semmes from Euclidean spaces to complete metric measure spaces with controlled geometry (Ahlfors regularity and supporting a Poincar\'e inequality). In particular, we find sharp…

B. Toen defined a Riemann-Roch map from the rational algebraic K-theory of a tame Deligne-Mumford quotient stack to the \'etale K-theory of its inertia. He proved that this map is an isomorphism and that it is covariant with respect to…

Given a symplectic manifold $(M,\omega)$ admitting a metaplectic structure, and choosing a positive $\omega$-compatible almost complex structure $J$ and a linear connection $\nabla$ preserving $\omega$ and $J$, Katharina and Lutz Habermann…

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply…

In this paper we study the relationship between the extended symmetries of exact Courant algebroids over a manifold $M$, defined by Bursztyn, Cavalcanti and Gualtieri, and the Poisson algebras of admissible functions associated to twisted…

We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other…

We consider a compact Riemann surface $R$ of arbitrary genus, with a finite number of non-overlapping quasicircles, which separate $R$ into two subsets: a connected Riemann surface $\Sigma$, and the union $\mathcal{O}$ of a finite…

We apply a version of the Chas-Sullivan-Cohen-Jones product on the higher loop homology of a manifold in order to compute the homology of the spaces of continuous and holomorphic maps of the Riemann sphere into a complex projective space.…

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…

We study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH = 0, which appears in string theory compactification scenarios. By using the identification…

In this paper we prove several related results concerning smooth $\Z_p$ or $\s^1$ actions on 4-manifolds. We show that there exists an infinite sequence of smooth 4-manifolds $X_n$, $n\geq 2$, which have the same integral homology and…

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian…

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a…

For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In…

Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In this paper, we point out…

We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a…

Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular,…

We study exact orbifold fillings of contact manifolds using Floer theories. Motivated by Chen-Ruan's orbifold Gromov-Witten invariants, we define symplectic cohomology of an exact orbifold filling as a group using classical techniques, i.e.…