Related papers: Intermediate Jacobians and Burnside invariants
We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…
A new quantum gauge model is proposed. From this quantum gauge model we derive a quantum invariant of 3-manifolds. We show that this quantum invariant of 3-manifolds gives a classification of closed (orientable and connected) 3-manifolds.…
We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees.…
We continue to develop an obstruction theory for embedding 2-spheres into 4-manifolds in terms of Whitney towers. The proposed intersection invariants take values in certain graded abelian groups generated by labelled trivalent trees, and…
We give two characterizations of Jacobians of curves with involution having fixed points in the framework of two particular cases of Welter's trisecant conjecture. The geometric form of each of these characterizations is the statement that…
A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of these abelian varieties, and thus give a description of…
This monograph studies $KK$-theory in its unbounded model. The central object is the $KK$-bordism group obtained by imposing the $KK$-bordism relation on unbounded $KK$-cycles. In the paradigm of noncommutative geometry, an unbounded…
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
We prove that the intermediate Jacobian of the Klein quartic $3$-fold $X$ is not isomorphic, as a principally polarized abelian variety, to a product of Jacobians of curves. As corollaries we deduce (using a criterion of Clemens-Griffiths)…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…
In this paper, we introduce a rational $\tau$ invariant for rationally null-homologous knots in contact 3-manifolds with nontrivial Ozsv\'{a}th-Szab\'{o} contact invariants. Such an invariant is an upper bound for the sum of rational…
We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by…
This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.
We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for etale gerbes over such stacks.
The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In…
Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…
In this paper, we study non-commutative projective schemes whose associated non-commutative graded algebras are finite over their centers. We study their moduli spaces of stable sheaves, and construct a symmetric obstruction theory in the…
Let $\Sigma$ be a smooth projective complex curve and $\mathfrak{g}$ a simple Lie algebra of type ${\sf ADE}$ with associated adjoint group $G$. For a fixed pair $(\Sigma, \mathfrak{g})$, we construct a family of quasi-projective Calabi-Yau…
This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of…