相关论文: Loop space decompositions of highly symmetric spac…

We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.

In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral join complexes. Then we compute the universal algebra of polyhedral join complexes under certain split conditions and…

Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincar\'e Duality complexes has yielded new methods for analysing the homotopy theory of manifolds. In this paper we will expand upon these methods,…

In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral product complexes. Then we compute the universal algebra of polyhedral product complexes under certain split…

We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space,…

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…

Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form $D + SP^{n-d}(X)$ in symmetric products $SP^n(X)$ where $D\in SP^d(X)$. As an…

We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topology, and the study of…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…

In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The…

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic…

We construct a smooth symmetric compactification of the space of all labeled tetrahedra in P^3.

`Loop-fusion cohomology' is defined on the continuous loop space of a manifold in terms of \vCech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that…

A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…

Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. Symmetric products of punctured surfaces are Liouville manifolds of interest e.g. for Heegaard Floer theory. We study the…

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then its complexification has a hypercomplex structure. It is…

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…

We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine…

We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the…