Related papers: Unimodal generalized pseudo-Anosov maps

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…

Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for pseudo-holomorphic maps from the cylinder S to an…

It is known that there is at least an invariant analytic curve passing through each of the components in the complement of nodal singularities, after the reduction of singularities of a germ of singular foliation in ${\mathbb C}^2,0$}.…

We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space.…

We use new homotopy-theoretic tools to prove the existence of smooth $U(1)$- and $Sp(1)$-actions on infinite families of exotic spheres. Such families of spheres are propagated by the complex and quaternionic analogues of the Mahowald…

Anosov representations $\rho$ of a hyperbolic group $\Gamma$ into a semisimple Lie group $G$ are known to admit cocompact domains of discontinuity in flag varieties $G/Q$, endowing the compact quotient manifolds $M_\rho$ with a…

In this paper, we are concerned with interactions between isoparametric theory and differential topology. Two foliations are called equivalent if there exists a diffeomorphism between the foliated manifolds mapping leaves to leaves. Using…

Andersen, Masbaum and Ueno conjectured that certain quantum representations of surface mapping class groups should send pseudo-Anosov mapping classes to elements of infinite order (for large enough level $r$). In this paper, we relate the…

We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be…

We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…

We study the behavior of hyperbolic affine automorphisms of a translation surface which is infinite in area and genus that is obtained as a limit of surfaces built from regular polygons studied by Veech. We find that hyperbolic affine…

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

We study the notion of symplectic scalar curvature on the supermanifold over an ordinary Fedosov manifold whose structural sheaf is that of differential forms. In this purely geometric context, we introduce two families of odd super-Fedosov…

We study the topology and geometry of compact complex manifolds associated to Anosov representations of surface groups and other hyperbolic groups in a complex semisimple Lie group $G$. These manifolds are obtained as quotients of the…

This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish…

We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the 2-torus. From that, we also explore how the regularity of the stable and unstable foliations implies smooth conjugacy inside a class of…

We construct algebraic families of exotic affine 3-spheres, that is, smooth affine threefolds diffeomorphic to a non-degenerate smooth complex affine quadric of dimension 3 but non algebraically isomorphic to it. We show in particular that…

We have proved that homeomorphisms of domains of Euclidean space, inverse of which distort the modulus of families of curves by Poletskii type, have a continuous extension to isolated boundary point.

We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…

Let phi be a pseudo-Anosov flow on a closed oriented atoroidal 3-manifold M. We show that if F is any taut foliation almost transverse to phi, then the action of pi_1(M) on the boundary of the flow space, together with a natural collection…