Related papers: E2 formality via obstruction theory
We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.
It is a prominent conjecture (relating Riemannian geometry and algebraic topology) that all simply-connected compact manifolds of special holonomy should be formal spaces, i.e., their rational homotopy type should be derivable from their…
We describe algebraic obstruction theories for realizing an abstract coalgebra K_* over the mod p Steenrod algebra as the homology of a topological space, and for distinguishing between the p-homotopy types of different realizations. The…
We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms…
We analyze the algebraic structures of G--Frobenius algebras which are the algebras associated to global group quotient objects. Here G is any finite group. These algebras turn out to be modules over the Drinfeld double of the group ring…
We observe that the Poincare duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq^1, Sq^2, and Sq^4 on the…
We invent a new cohomology theory for Lie triple algebras. Using this cohomology, we introduce the notions of 2-term $L_\infty$-triple algebras and Lie triple 2-algebras. We prove that the category of 2-term $L_\infty$-triple algebras is…
We introduce coG_2-vector fields, coRochesterian 2-forms and coRochesterian vector fields on manifolds with a coclosed G_2-structure as a continuous of work from [15], and we show that the spaces of coG_2-vector fields and of coRochesterian…
Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map…
The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of N=2 superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge…
Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…
We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric…
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
The main purpose of this paper is to study restricted formal deformations of restricted Lie-Rinehart algebras in positive characteristic $p$. For $p>2$, we discuss the deformation theory and show that deformations are controlled by the…
Let X be a smooth variety over a number field k embedded as a degree d subvariety of $\mathbb{P}^n$ and suppose that X is a counterexample to the Hasse principle explained by the Brauer-Manin obstruction. We consider the question of whether…
A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
We classify group gradings on the simple Lie algebras of types $G_2$ and $D_4$ over the field of real numbers (or any real closed field): fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism.
Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.