Related papers: Toric origami structures on quasitoric manifolds

For a simple $n$-polytope $P$, a quasitoric manifold over $P$ is a $2n$-dimensional smooth manifold with a locally standard action of the $n$-dimensional torus for which the orbit space is identified with $P$. This paper shows the…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…

We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…

The parameter-space orbifold construction of open and unoriented toroidal and (target-space) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral four-dimensional type-I…

Consider an algebraic torus of small dimension acting on an open subset of a complex vector space, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is…

In this note, we give a list of all non-isomorphic quasitriangular structures on the 8-dimension Kac algebra K_8.

We classify closed, simply connected $n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2\leq n\leq 6$. In dimensions $3k$, $k=1,2$ there is only one such manifold…

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum…

We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.

Every cohomology ring isomorphism between two non-singular complete toric varieties and quasitoric manifolds, respectively, with second Betti number $2$ is realizable by a diffeomorphism and homeomorphism, respectively.

A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991 Duke paper. There they extensively studied topological invariants of quasitoric manifolds. These manifolds are generalizations or topological counterparts of…

In this paper we show that there exist simply connected symplectic 4-manifolds which contain infinitely many knotted lagrangian tori, i.e. lagrangian embeddings of tori that are homotopic but not isotopic. Moreover, the homology class they…

In this paper we describe the general theory of constructing toroidal compactifications of locally symmetric spaces and using these to compute dimension formulas for spaces of modular forms. We focus explicitly on the case of the orthogonal…

We identify a certain universal Landau-Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the primitive form are constructed via Seidel…