Related papers: A Twisted sl_2(C) Isomonodromic-Isospectral Corres…

Let $M$ be a connected compact orientable surface, $f:M\to \mathbb{R}$ be a Morse function, and $h:M\to M$ be a diffeomorphism which preserves $f$ in the sense that $f\circ h = f$. We will show that if $h$ leaves invariant each regular…

We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to…

The isomonodromic deformations underlying the Painlev\'e transcendants are interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop algebra $\tilde\grg$ in the classical $R$-matrix framework. It is shown how canonical…

We provide a new construction of the topological cyclic homology $TC(C)$ of any spectrally-enriched $\infty$-category $C$, which affords a precise algebro-geometric interpretation of the cyclotomic trace map $K(X) \to TC(X)$ from algebraic…

This is a sequel to the paper \cite{MO-mw} which identified maximally writhed algebraic links in $\rp^3$ and classified them topologically. In this paper we prove that all maximally writhed links of the same topological type are rigidly…

A systematic program is developed for analyzing and cancelling local anomalies on networks of intersecting orbifold planes in the context of M-theory. Through a delicate balance of factors, it is discovered that local anomaly matching on…

In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relatively simple behaviour it was known that such a classification…

Isospectrality of planar domains which are obtained by successive unfolding of a fundamental building block is studied in relation to iso-length spectrality of the corresponding domains. Although an explicit and exact trace formula such as…

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain…

We consider real isotropic geodesics on manifolds endowed with a pseudoconformal structure and their applications to the theory of lightlike hypersurfaces on such manifolds, the geometry of four-dimensional conformal structures of…

There is an abundance of equations of Painlev\'e type besides the classical Painlev\'e equations. Classifications have been computed by the Japanese school. Here we consider Painlev\'e type equations induced by isomonodromic families of…

Using the Fourier-Laplace transform, we describe the isomonodromy equations for meromorphic connections on the Riemann sphere with unramified irregular singularities as those for connections with a (possibly ramified) irregular singularity…

In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This…

A subspace or subgroup is isotropic under a bilinear map if the restriction of the map on it is trivial. We study maximal isotropic subspaces or subgroups under skew-symmetric maps, and in particular the isotropy index---the maximum…

We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also…

Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface $S$ endowed with a holomorphic symplectic form $\omega$ and a projection onto $\mathbb{C}$. We provide a full…

In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…

We show that the equivariant chain complex associated to a minimal CW-structure X on the complement M(A) of a hyperplane arrangement A, is independent of X. When A is a sufficiently general linear section of an aspheric arrangement, we…