arXiv research

Constructs harmonic maps between special geometric shapes.

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Paper proves existence and gives construction of Symphonic map between ellipsoids.

The paper constructs biharmonic maps between spheres using polynomial maps.

New subgroups of mapping class groups constructed for infinite-type surfaces.

Constructs a moment map flow for isotropic maps on surfaces.

In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group H that minimise a mean distortion functional. We propose to construct such mappings by considering a corresponding problem between domains of Poincaré half-plane $\mathbb H$. The first map we construc…

This paper constructs real algebraic maps that are topologically special generic maps.

Paper constructs Thom-Smale complex using instantons from Morse functions.

We give a new description of the Arnoux-Yoccoz mapping classes as a product of two Dehn twists and a finite order element. The construction is analogous to Penner's construction of mapping classes with small stretch factors.

Extends Satoh's map to virtual m-links and constructs geometric pictures.

Paper constructs fold maps with useful singular value sets.

Lagrange's map construction ideas influenced later mathematicians.

{\it Fold maps} are fundamental tools in generalizing the theory of Morse functions and its application to studies of geometric properties of manifolds. One of the fundamental and important problems in the theory of fold maps is to construct explicit fold maps, which are often difficult. In this paper, we construct new…

The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.

Construct pseudo-Anosovs from expanding interval maps, reconciling Thurston's construction.

Propose a new 3d quantum trace map that agrees with Garoufalidis and Yu's construction and extends to certain manifolds with ideal triangulated boundaries.

In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes special generic maps on spheres and such maps have been constructed on smooth bundles …

New boundary constructed for mapping class group.

Wave maps (or Lorentzian-harmonic maps) from a $1+1$-dimensional Lorentz space into the $2$-sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-space via the Gauss map, which is harmonic with respect to the metric induced by the second fundamental form. We give a method for constructin…

The paper constructs simplicial maps of any degree on spheres, solving a long-standing problem.

Develops methods to construct harmonic and wave maps into variable-curvature surfaces.

We give a Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of -1 codimensional stable maps with prescribed singular fibers.

We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using the branched covering of the genus two surface over the sphere an…

This thesis extends Hamiltonian actions to multisymplectic geometry, classifying actions on spheres and constructing homotopy comomentum maps.

We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner's construction lie off the unit circle. As a consequence, we show that for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner's construc…

Computes minimal dilatation for Thurston maps on surfaces.

In this paper we construct gluing maps and cobordism maps for sutured monopole Floer homology.

Visual construction of maps linking to two-bridge links.

Koschorke introduced a map from the space of closed $n$-component links to the ordered configuration space of $n$-tuples of points in $\mathbb{R}^3$, and conjectured that this map separates homotopy links. The purpose of this paper is to construct an analogous map for string links, and to prove (1) this map in fact sep…

Constructs stable maps from 3-manifolds to surfaces without cusps.

New method for triharmonic maps to spheres in various dimensions.

New construction method for special geometric structures.

Introduces quasi-holomorphic maps and their properties.

Researchers construct an index map for contact manifolds using K-theory.

The study restricts manifolds with certain explicit SGL maps and constructs them.

Constructs a moment map for maps to balanced manifolds.

Quantum Frobenius map for $SL_3$ skein modules constructed and described.

Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than $2-$Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that none of these are vertex transitive. We establish existence of 12-covered triangula…

We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of …

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour…

The paper explores continuous limits of pentagram maps and their relation to KdV equations.

Researchers extend period maps for Calabi-Yau types using modified Kato-Nakayama-Usui construction.

Given a non-compact Riemannian manifold M and a submanifold N of codimension q, we will construct under certain assumptions on both M and N a wrong way map in uniformly finite homology. Using an equivariant version of the construction and applying it to universal covers, we will construct wrong way maps in homology of …

In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics on $\mathbb{R}$-trees: one geometric and one algebraic. The geometric constructio…

We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of symmetries. The periodic mapping classes can in turn be used to construct sequences of pse…

Maps self-duality in little disks operad to framed manifolds.

Biharmonic maps between surfaces are studied in this paper. We compute the bitension field of a map between surfaces with conformal metrics in complex coordinates. As applications, we show that a linear map from Euclidean plane into $(\mathbb{R}^2, σ^2dwd\bar w)$ is always biharmonic if the conformal factor $σ$ is bi-a…