Related papers: String bordism and chromatic characteristics
In recent work Kachru, Kumar and Silverstein introduced a special class of non-supersymmetric type II string theories in which the cosmological constant vanishes at the first two orders of perturbation theory. Heuristic arguments suggest…
We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…
We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and…
The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural…
Let GO(2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic not equal to 2. We determine the etale cohomology ring with mod 2 coefficients of the algebraic stack BGO(2n). In…
The perturbative analysis of models of open and closed superstrings presents a number of surprises. For instance, variable numbers of antisymmetric tensors ensure their consistency via generalized Green-Schwarz cancellations and a novel…
Kotschick and Morita recently discovered factorisations of characteristic classes of transversally symplectic foliations that yield new characteristic classes in foliated cohomology. We describe an alternative construction of such…
We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum L_{K(2)S^0 as the inverse limit of a tower of fibrations…
We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…
We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is closely related to the topological Andre-Quillen homology…
Topologically ordered phases of matter display a number of unique characteristics, including ground states that can be interpreted as patterns of closed strings. In this paper, we consider the problem of detecting and distinguishing closed…
We calculate the structure of the finitely-generated groups H_2(SL_2(Z[1/m])) when m is a multiple of 6. We construct explicit homology classes which generate these groups and have prescribed orders. When n is at least 2 and m is the…
In this paper, we characterize the second bounded characteristic classes of foliated bundles in terms of the non-descendible quasi-morphisms on the universal covering of the structure group. As its application, we study the boundedness of…
The primary interest of this paper is to discuss the role of twisting cochains in the theory of characteristic classes. We begin with the homological description of monodromy map, associated with a connection on a trivial bundle over a…
Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori,…
We compute the cohomology with trivial coefficients of Lie algebras $\mathfrak{m}_0$ and $\mathfrak{m}_2$ of maximal class over the field $\mathbb{Z}_2$. In the infinite-dimensional case, we show that the cohomology rings…
We discuss the role of string solitons in duality and examine the feature of compositeness, which allows for the interpretation of general solutions as bound states of supersymmetric fundamental constituents. This feature lies at the heart…
Let $\Gamma$ be a discrete group. Assuming rational injectivity of the Baum-Connes assembly map, we provide new lower bounds on the rank of the positive scalar curvature bordism group and the relative group in Stolz' positive scalar…
Preliminary investigations of the topological phase of string theory along the lines of a (restricted) $\dot{w}_{\infty}$ non-linear sigma model are provided. Gauge fixing the w gravity gauge fields by preserving a geometric identity Lorenz…
Working over an algebraically closed field of characteristic zero, we compute the cohomology of the subalgebra A(2) of the motivic Steenrod algebra that is generated by Sq^1, Sq^2, and Sq^4. The method of calculation is a motivic version of…