有序配置空间与扭曲交换因子代数的高阶表示稳定性

The factorization theory of Thom spectra and twisted non-abelian Poincaré duality

We give a description of the factorization homology and $E_n$ topological Hochschild cohomology of Thom spectra arising from $n$-fold loop maps $f: A \to BO$, where $A = Ω^n X$ is an $n$-fold loop space. We describe the factorization homology $\int_M Th(f)$ as the Thom spectrum associated to a certain map $\int _M A \to BO$. When $M$ is framed and $X$ is $(n-1)$-connected, this spectrum is equivalent to a Thom spectrum of a virtual bundle over the mapping space $Map_c(M,X)$; in general, this is a Thom spectrum of a virtual bundle over a certain section space. This can be viewed as a twisted fo…

Dirac Families for Loop Groups as Matrix Factorizations

We identify the category of integrable lowest-weight representations of the loop group LG of a compact Lie group G with the linear category of twisted, conjugation-equivariant curved Fredholm complexes on the group G: namely, the twisted, equivariant matrix factorizations of a super-potential built from the loop rotation action on LG. This lifts the isomorphism of K-groups of [FHT1,2, 3] to an equivalence of categories. The construction uses families of Dirac operators.

Twisted Kähler differential forms

We construct a braided structure on the algebra of Kähler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see http://www.math.jussieu.fr/~karoubi, for topological purposes.

Etale twists in noncommutative algebraic geometry and the twisted Brauer space

This paper studies etale twists of derived categories of schemes and associative algebras. A general method, based on a new construction called the twisted Brauer space, is given for classifying etale twists, and a complete classification is carried out for genus 0 curves, quadrics, and noncommutative projective spaces. A partial classification is given for curves of higher genus. The techniques build upon my recent work with David Gepner on the Brauer groups of commutative ring spectra.

Factorization homology and calculus à la Kontsevich Soibelman

Using factorization homology techniques, we give a simple proof of the action of Kontsevich and Soibelman operad on the pair consisting of Hochschild cohomology and Hochschild homology. The proof obviously extends to higher Hochschild cohomology and factorization (also called chiral) homology. Note that our result works in categories of chain complexes but also in categories of modules over a commutative ring spectrum.

分解同调的HKR定理

An HKR theorem for factorization homology

本文证明了一个HKR定理，用于计算光滑交换环谱的分解同调，修正并推广了McCarthy-Minasian的THH计算，并应用于有理KU的高阶THH。