Related papers: H-infinity is not E-infinity

We give a source of examples of H_infinity ring structures that do not lift to E_infinity ring structures, based on Mandell's equivalence between certain cochain algebras and spaces.

The construction of E infinity ring spaces and thus E infinity ring spectra from bipermutative categories gives the most highly structured way of obtaining the K-theory commutative ring spectra. The original construction dates from around…

In "Elliptic spectra, the Witten genus, and the Theorem of the cube" (Invent. Math. 146 (2001)), the authors constructed a natural map from the Thom spectrum MU<6> to any elliptic spectrum, called the "sigma orientation". MU<6> is an…

The space of E-infinity structures on an simplicial operad C is the limit of a tower of fibrations, so its homotopy is the abutment of a Bousfield-Kan fringed spectral sequence. The spectral sequence begins (under mild restrictions) with…

E infinity ring spectra were defined in 1972, but the term has since acquired several alternative meanings. The same is true of several related terms. The new formulations are not always known to be equivalent to the old ones and even when…

In this note, we prove an obstruction theorem for the existence of A infinite-structures over a commutative ring R on an algebra A associative up to homotopy, in terms of the Hochschild cohomology of the associative algebra H(A). The hidden…

We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…

In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of…

Spectrum is an important numerical invariant of an isolated hypersurface singularity, connecting its topological and analytic structures. The well-known Hertling conjecture tells the relation of range and variance of exponents i.e. elements…

An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.

We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that there are only finitely many possibilities. As a corollary we…

A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.

We introduce a notion of characteristic for connective $p$-local $E_\infty$ ring spectra and study some basic properties. Apart from examples already pointed out by Markus Szymik, we investigate some examples built from Hopf invariant $1$…

We prove that any spectrum is equivalent to the nonconnective K-theory of a stable $\infty$-category. We use these results to construct a stable $\infty$-category $\mathcal{C}$ with a bounded t-structure such that…

Given an SFT $\Sigma$ and a finite set $S$ of finite words, let $\Sigma\langle S\rangle$ denote the subshift of $\Sigma$ that avoids $S$. We establish a general criterion under which we can bound the entropy perturbation…

We isolate a large class of self-adjoint operators H whose essential spectrum is determined by their behavior at large x and we give a canonical representation of their essential spectrum in terms of spectra of limits at infinity of…

This paper is a continuation of the study of spectral flow inside essential spectrum initiated in \cite{AzSFIES}. Given a point $\lambda$ outside the essential spectrum of a self-adjoint operator $H_0,$ the resonance set, $\mathcal…

We define A-infinity-bimodules similarly to Tradler and show that this notion is equivalent to an A-infinity-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground…