Related papers: Category of Noncommutative CW complexes. III

The purpose of this paper is to establish several new results about the Hodge theory of Lagrangian fibrations on (not necessarily compact) holomorphic symplectic manifolds. Let $M$ be a holomorphic symplectic manifold of dimension $2n$ that…

Let $\mathrm{k}_{0}$ be a field and $W$ a finite orthogonal reflection group over $\mathrm{k}_{0}$. We prove Serre's splitting principle for cohomological invariants of $W$ with values in Rost's cycle modules (over $\mathrm{k}_{0}$) if the…

In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems…

We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous…

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

We extend the spectral theory of commutative C*-categories to the non full-case, introducing a suitable notion of spectral spaceoid provinding a duality between a category of "non-trivial" *-functors of non-full commutative C*-categories…

We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression forms as well as a differential refinement of the smooth…

Suppose $X$ is a smooth projective scheme of finite type over a field $K$, $\mathcal{E}$ is a locally free ${\mathcal{O}}_{X}$-bimodule of rank 2, $\mathcal{A}$ is the non-commutative symmetric algebra generated by $\mathcal{E}$ and ${\sf…

We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that $C\ot D$ is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two…

We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the…

For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain…

The Swan, Leray and Leray-Serre spectral sequences of a compact Hausdorff HLC space acted on by a discrete group are shown to be isomorphic.

We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the…

Let $\mathbb{F}$ be a fixed field and let $X$ be a simplicial complex on the vertex set $V$. The Leray number $L(X;\mathbb{F})$ is the minimal $d$ such that for all $i \geq d$ and $S \subset V$, the induced complex $X[S]$ satisfies…

Using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec R admits a toric non-commutative crepant resolution (NCCR). We give an alternative proof of this result by constructing a…

Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We…

Let $G$ be a Lie-group and $\Ga\subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\om$ of $\Ga$ we show that the $G$-representation on $L^2(\Ga\bs G,\om)$ admits a complete filtration with…

In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)-graded cohomology for finite groups G. Special attention is paid to the case G=Z/2 where the spectral sequence is used to compute…

We prove the existence of a spectral sequence for Lagrangian Floer homology which converges to the Floer homology of the image of a Lagrangian submanifold under multiple fibred Dehn twists. The $E_1$ term of the sequence is given by the…

For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…