Related papers: Complex cobordism of involutions
We characterize all varieties with a torus action of complexity one that admit iteration of Cox rings.
We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic…
Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.
We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8…
We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…
In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of…
We prove an existence result for exact lagrangian cobordisms between closed legendrians.
We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…
In this paper we survey results and recent progresses on the equivariant bordism classification of 2-torus manifolds and unitary toric manifolds.
Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.
We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…
We exploit various inclusions of algebraic groups to give a new construction of groups of type E8, determine the Killing forms of the resulting E8's, and define an invariant of central simple algebras of degree 16 with orthogonal involution…
We introduce quiver representation-valued invariants of oriented virtual knots and links associated to a choice of finite virtual biquandle, abelian group, set of virtual Boltzmann weights, commutative unital ring and set of virtual…
We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie…
This paper is an introduction to the use of the cobordism of chain complexes with Poincar\'e duality in surgery theory. It is a companion to the author's paper "An introduction to algebraic surgery" math.AT/0008071 (to appear in Volume 2 of…
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…
In this paper we caculate mod 2 cohomology ring of $F_{\mathbb{Z}_2^m}(\mathbb{R}^m,n)$ , which is local representation of orbit congfiguration spaces over small covers. We construct a differntial graded algebra, and there is a ring…
Let $C_2$ denote the cyclic group of order two. Given a manifold with a $C_2$-action, we can consider its equivariant Bredon $RO(C_2)$-graded cohomology. In this paper, we develop a theory of fundamental classes for equivariant submanifolds…
Group presentations are implicit descriptions of 2-dimensional cell complexes with only one vertex. While such complexes are usually sufficient for topological investigations of groups, multi-vertex complexes are often preferable when the…