相关论文: Multiplicative structures on homotopy spectral seq…

The purpose of this note is prove that the mixed Hodge structure constructed by the author in math.AG/0301140 [The Leray spectral sequence is motivic, Invent. 2005] for geometric variations of Hodge structure coincides with the structure…

We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…

We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.

Manifold calculus of functors has in recent years been successfully used in the study of the topology of various spaces of embeddings of one manifold in another. Given a space of embeddings, the theory produces a Taylor tower whose purpose…

We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.

This review paper summarizes the contents of the talk given by the author at the 8th International Congress of Chinese Mathematicians. Using examples of Schr\"odinger operators on metric graphs, it is shown that a nontrivial topology of the…

The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this…

Homotopy coherence has a considerable history, albeit also by other names. We provide a brief semi-historical survey providing some links that may not be common knowledge.

Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…

We work out the details of a correspondence observed by Goodwillie between cosimplicial spaces and good functors from a category of open subsets of the interval to the category of compactly generated weak Hausdorff spaces. Using this, we…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…

Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…

We investigate how the spectral and topological properties of electron systems evolve on a lattice that interpolates between the honeycomb and its 1/6-depleted structures through the introduction of selective random defects. We find that in…

We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving $\omega$-categoricity and Ehrenfeuchtness under these combinations are…

A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical…