Related papers: A spectral sequence for string cohomology
Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…
In a recent preprint, Sakellaridis and Venkatesh considered the spectral decomposition of the space $L^2(X)$, where $X = H\G$ is a spherical variety and $G$ is a real or $p$-adic group, and stated a conjecture describing this decomposition…
We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string's spacetime Lorentz algebra commutes with a certain inductive…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
We prove that the stabilization of spaces functor---the classical construction of associating a spectrum to a pointed space by tensoring with the sphere spectrum---satisfies homotopical descent on objects and morphisms. This is the…
The Heisenberg Lie algebras over an algebraically closed field F of characteristic p > 0 always admit a family of restricted structures. We use the ordinary 1- and 2-cohomology spaces with adjoint coefficients to compute the restricted 1-…
Let $X$ be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ of the free loop…
We present a spectral sequence for free isometric Lie algebra actions (and consequently locally free isometric Lie group actions) which relates the de Rham cohomology of the manifold with the Lie algebra cohomology and basic cohomology…
We prove that if two closed disks X_1 and X_2 of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X_1\cap X_2 is a complete (2+2/\sqrt{3})-spectral set for A. When the…
We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A together with an explicit functor from the category of…
Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional…
We compute the $E_2$ page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg-MacLane space, $ko_*(K(Z/2,2))$. This required a careful analysis of the structure of $H^*(K(Z/2,2);Z_2)$ as a…
Models with axion like particles (ALPs) often predict the formation of a string-domain wall network in the early universe. We study how such networks of defects appear in the context of string theory, and discuss the conditions for their…
The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}P^n$ are computed along with the Atiyah-Hirzebruch spectral sequence for $ER(2)^*(\mathbb{C}P^\infty)$. This, along with other papers in this series, gives us the…
We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…
We introduce a common domain of definition for the loop product and the loop coproduct, reduced loop homology, on which they combine to a unital infinitesimal anti-symmetric bialgebra structure. In particular, a relation conjectured by…
We discuss the semi-classical perturbation spectra produced in the massless fields of the low energy string action in a pre big bang type scenario. Axion fields may possess an almost scale-invariant spectrum on large scales dependent upon…
We recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local coefficients. We then show how to construct new equivariant…
We study how the combinatorial structure of the Salvetti complexes of the braid arrangements are related to homotopy theoretic properties of iterated loop spaces. We prove the skeletal filtrations on the Salvetti complexes of the braid…
Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…