相关论文: Recent Developments in Line Bundle Cohomology and …

Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…

This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

The weakly coupled vacuum of $E_8\otimes E_8$ heterotic string theory remains an attractive scenario for phenomenolgy and cosmology. The particle spectrum is reviewed and the issues of gauge coupling unification, dilaton stabilization and…

Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…

We study the spaces of string links and homotopy string links in an arbitrary manifold using multivariable manifold calculus of functors. We construct multi-cosimplicial models for both spaces and deduce certain convergence properties of…

For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of…

An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key…

We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized…

Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…

In this paper we study the cohomological criterion for the splitting of vector bundles on multiprojective spaces $\mathbb{P}^{n_1}\times\ldots\times\mathbb{P}^{n_s}$. We also give a generalization of vanishing cohomological criteria for…

We study the cohomology of spaces of string links and braids in $\mathbb{R}^n$ for $n\geq 3$ using configuration space integrals. For $n>3$, these integrals give a chain map from certain diagram complexes to the deRham algebra of…

This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research. We begin…

In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather…

Peptide strings have been developed as a concept for the past fourteen years. They are proposed to basically entail various quantum states engendered by the physical interactions of proteins containing peptide portions that are similar to…

Tautological bundles of realizations of matroids were introduced in [BEST23] as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmetric powers of these vector bundles, and show that they…

We use a generalization of Horrocks monads for arithmetic Cohen-Macaulay (ACM) varieties to establish a cohomological characterization of linear and Steiner bundles over projective spaces and quadric hypersurfaces. We also study resolutions…

We develop a theory of Finite Element Systems, for the purpose of discretizing sections of vector bundles, in particular those arizing in the theory of elasticity. In the presence of curvature we prove a discrete Bianchi identity. In the…

The aim of this paper is to study the cohomology theory of monoid schemes in general and apply it to vector and line bundles. We will prove that over separated monoid schemes, any vector bundle is a coproduct of line bundles and then go on…

This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…