Related papers: Rational curvature invariants for 2-complexes
We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.
In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most…
We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure three-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the…
We give a formula for the cohomological invariants of a root stack, which we apply to compute the cohomological invariants and the Brauer group of the stack of admissible double coverings.
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…
We show that measures of irrationality on very general codimension two complete intersections and very general complete intersection surfaces are multiplicative in the degrees of the defining equations. This confirms some cases of a…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
A clover is a framed trivalent graph with some additional structure, embedded in a 3-manifold. We define surgery on clovers, generalizing surgery on Y-graphs used earlier by the second author to define a new theory of finite-type invariants…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
This is meant to be a survey article for the Cubo Journal. We discuss the existence and number of rational points over a finite field, the Hodge type over the complex numbers, and the motivic conjectures which are controlling those…
This is a survey of the rationality problem in invariant theory. It also contains some new results, in particular in Chapter 2 on moduli spaces of plane curves with a theta-characteristic, and a detailed account of the relation of the…
We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…