Related papers: On the 2-loop part of the Johnson cokernel

We prove the Cartan-Eilenberg stable elements theorem and construct a Lyndon-Hochschild-Serre type spectral sequence for pro-fusion systems. As an application, we determine the continuous mod-$p$ cohomology ring of…

Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons,…

A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bi-complex where one of the two operators is the classical $\overline\partial$-operator, while the other operator is the adjoint action of the…

We provide algorithms for computing the Rochlin invariants of mod 2 homology spheres and mapping tori. This provides a unified framework for studying two families of maps: the Birman-Craggs maps of the Torelli group, and Sato's maps of the…

A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain…

We first develop a general theory of Johnson filtrations and Johnson homomorphisms for a group $G$ acting on another group $K$ equipped with a filtration indexed by a "good" ordered commutative monoid. Then, specializing it to the case…

Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_{\alpha}\times \Sigma$ near singular…

We exhibit the Hodge degeneration from nonabelian Hodge theory as a $2$-fold delooping of the filtered loop space $E_2$-groupoid in formal moduli problems. This is an iterated groupoid object which in degree $1$ recovers the filtered circle…

We express the rational cohomology of the unordered configuration space of a compact oriented manifold as a representation of its mapping class group in terms of a weight-decomposition of the rational cohomology of the mapping space from…

We establish Monod's isomorphism conjecture in degree-three bounded cohomology for every complex simple Lie group of classical type. Our main ingredient is a bounded-cohomological stability theorem with an optimal range in degree three that…

This paper can be seen as an update to part of the author's dissertation. We study the mod $p$ cohomology of the pro-$p$ Iwahori subgroups $I$ of $\operatorname{SL}_{n}(\mathbb Q_{p})$ (and $\operatorname{GL}_{n}(\mathbb{Q}_{p})$) for $n=2$…

Let $S$ be a closed orientable spin manifold. Let $K \subset S$ be a submanifold and denote its complement by $M_K$. In this paper we prove that there exists an isomorphism between partially wrapped Floer cochains of a cotangent fiber…

We calculate the two-loop quantum corrections, including the back-reaction of the Hawking radiation, to the one-loop effective metric in a unitary gauge quantization of the CGHS model of 2d dilaton gravity. The corresponding evaporating…

Given a finite quandle, we introduce a quandle homotopy invariant of knotted surfaces in the 4-sphere, modifying that of classical links. This invariant is valued in the third homotopy group of the quandle space, and is universal among the…

We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomorphisms/maps, called the p-Johnson homomorphisms/maps,…

We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probability measure, we study the topological structure of the…

This thesis is split up into two parts: The first one concerns (pseudo)-holomorphic Hamiltonian systems, while the second part is about K\"ahler structures of complex coadjoint orbits. We begin the first part by investigating basic…

This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1.…

A model of hard-core bosons and spin-1 sites with single-ion anisotropy is proposed to approximately describe hole pairs moving in a background of singlets and triplets with the aim of exploring the relationship between superconductivity…

The motion of a single hole in a 2D triangular antiferromagnet is investigated using the t-J model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function…