Related papers: Toda brackets and cup-one squares for ring spectra
We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the I-spaces, which are diagrams indexed by finite sets and injections, and J-spaces,…
We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant…
It is shown that the first and second homotopy groups of the $\eta$-inverted sphere spectrum over a field of characteristic not two are zero. A cell presentation of higher Witt theory is given as well, at least over the complex numbers.
This paper concerns the topology of isospectral real manifolds of certain Jacobi elements associated with real split semisimple Lie algebras. The manifolds are related to the compactified level sets of the generalized (nonperiodic) Toda…
We consider the Topological String/Spectral theory duality on toric Calabi-Yau threefolds obtained from the resolution of the cone over the $Y^{N,0}$ singularity. Assuming Kyiv formula, we demonstrate this duality in a special regime thanks…
If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then the cube induced by Goodwillie's integral cyclotomic trace from K(A) to TC(A) is homotopy cartesian. In other words, the homotopy fiber of the…
We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.
In this paper, it is shown that the Boolean ring of a commutative ring is isomorphic to the ring of clopens of its prime spectrum. In particular, Stone's Representation Theorem is generalized. The prime spectrum of the Boolean ring of a…
The paper concerns a compactification of the isospectral varieties of nilpotent Toda lattices for real split simple Lie algebras. The compactification is obtained by taking the closure of unipotent group orbits in the flag manifolds. The…
I provide an explicit construction of spectral curves for the affine $\mathrm{E}_8$ relativistic Toda chain. Their closed form expression is obtained by determining the full set of character relations in the representation ring of…
We establish a new representation of the infinite hierarchy of Pois- son brackets (PB) for the open Toda lattice in terms of its spectral curve. For the classical Poisson bracket (PB) we give a representation in the form of a contour…
Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…
The homotopy type and homotopy groups of some spectra TAF of topological automorphic forms associated to a unitary similitude group GU of type (1,1) are explicitly described in quasi-split cases. The spectrum TAF is shown to be closely…
It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is…
We extend the theory of Thom spectra and the associated obstruction theory for orientations in order to support the construction of the string orientation of tmf, the spectrum of topological modular forms. We also develop the analogous…
Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups…
In the present note we discuss two different ring structures on the set of holomorphic discrete series of a causal symmetric space of Cayley type $G/H$ and we suggest a new interpretation of Rankin-Cohen brackets in terms of intertwining…
We characterize ring spectra morphisms from the algebraic cobordism spectrum $\QTR{Bbb}{MGL}$ (\QCITE{cite}{}{Vo1}) to an oriented spectrum $\QTR{Bbb}{E}$ (in the sense of Morel \QCITE{cite}{}{Mo}) via formal group laws on the…
We analyze the functorial and multiplicative properties of the Thom spectrum functor in the setting of symmetric spectra, and we establish the relevant homotopy invariance.
We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.