Related papers: Algebraic cobordism and flag varieties

Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a $\Lambda$-tree. Analogous to the construction of graph $C^*$-algebras, we form a groupoid whose…

Let G denote a group and let W be an algebra over a commutative ring R. We will say that W is a G-graded twisted algebra (not necessarily commutative, neither associative) if there exists a G-grading W=\bigoplus_{g \in G}W_{g} where each…

For each simply connected, simple complex group $G$ we show that the direct sum of all vector bundles of conformal blocks on the moduli stack $\bar{\mathcal{M}}_{g, n}$ of stable marked curves carries the structure of a flat sheaf of…

Following the historical track in pursuing $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases,…

Let $P$ be an $n$-gon with $n\geq3.$ There is a formal combinatorial $A_\infty$-coalgebra structure on cellular chains $C_*(P)$ with non-vanishing higher order structure when $n\geq5$. If $X_g$ is a closed compact surface of genus $g\geq2$…

Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, i.e., lie…

Using a combinatorial approach which avoids geometry, this paper studies the ring structure of K_T(G/B), the T-equivariant K-theory of the (generalized) flag variety G/B. Here the data is a complex reductive algebraic group (or…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…

We determine the structure of the equivariant cohomology and $K$-theory of Bott towers. By restriction, we obtain similar results for Bott-Samelson varieties. This results allow us to describe more precisely the equivariant cohomology and…

The goal of this paper is to find a close to isomorphic presentation of 3-manifolds in terms of Hopf algebraic expressions. To this end we define and compare three different braided tensor categories that arise naturally in the study of…

We give a complete calculation of the cobordism ring of stably almost complex $C_p$-manifolds in terms of generators and relations. We also compare these generators with the geometrically-defined generators obtained by Kosniowski.

We define a graded twisted-coassociative coproduct on the tensor algebra $TW$ of any $\Z^n$-graded vector space $W$. If $W$ is the desuspension space $\da V$ of a graded vector space $V$, the coderivations (resp. quadratic ``degree 1''…

In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain torus actions on braid varieties and holomorphic symplectic…

Let C be a curve over a non-singular base variety S. We study algebraic cycles on the symmetric powers C^[n] and on the Jacobian J. The Chow homology of C^[*], the sum of all C^[n], is a ring using the Pontryagin product. We prove that this…

Van Daele and Wang developed a purely algebraic notion of weak multiplier Hopf algebras, which extends the notions of Hopf algebras, multiplier Hopf algebras, and weak Hopf algebras. With an additional requirement of an existence of left or…

In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense…

Given a reductive group, choice of maximal torus and Borel subgroup, and two subsets of the simple roots, one obtains a closed embedding of sub flag varieties. In this paper we compute the class of the sub flag variety in the Chow ring for…

Let $G$ be a simple, simply-connected complex algebraic group with Lie algebra $\mathfrak{g}$, and $G/B$ the associated complete flag variety. The Hochschild cohomology $HH^\bullet(G/B)$ is a geometric invariant of the flag variety related…

We define the Chow $t$-structure on the $\infty$-category of motivic spectra $SH(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $SH(k)^{c\heartsuit}$ when the exponential characteristic of $k$ is inverted.…

Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimension of $X$ and the order of $G$. An explicit…