Related papers: Birational invariants defined by Lawson homology
We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{\'a}r's {\em length} invariant.…
We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology. In particular,…
We study holomorphic foliations of codimension $k\geq 1$ on a complex manifold $X$ of dimension $n+k$ from the point of view of the exceptional minimal set conjecture. For $n\geq 2$ we show in particular that if the holomorphic normal…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…
In this paper, we construct an invariant for irreducible holomorphic symplectic manifolds of $K3^{[2]}$-type with antisymplectic involution by using the equivariant analytic torsion. Moreover, we give a formula for the complex Hessian of…
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…
A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This…
In this paper we compute Lawson homology groups and semi-topological K-theory for some threefolds and fourfolds. We consider smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected…
We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In…
A Riemannian manifold is a called a good rational expander in dimension $i$ if every $i$-cycle bounds a rational $i+1$-chain of comparatively small volume. We construct 3-manifolds which are good expanders in all dimensions. On the other…
Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…
We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin$^c$ structures, generalising the correction terms (or $d$--invariants) defined by Ozsv\'ath and…
We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…
The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…
Let V be a complete discrete valuation ring with uniformiser p. We introduce an invariant of Banach V-algebras called local cyclic homology. This invariant is related to analytic cyclic homology for complete, bornologically torsionfree…
This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi--Yau threefolds, defined by quivers with homogeneous…
We extend the covariant canonical formalism recently discussed in ref. [1] to geometric theories coupled to both bosonic and fermionic $p$-forms. This allows a covariant hamiltonian treatment of supergravity theories. As examples we present…
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove…
In [11] we showed that a loop in a simply connected compact Lie group $\dot{U}$ has a unique Birkhoff (or triangular) factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence…
In this article, using the recent theory of noncommutative motives, we compute the additive invariants of orbifolds (equipped with a sheaf of Azumaya algebras) using solely "fixed-point data". As a consequence, we recover, in a unified and…