Related papers: Updates on Hirzebruch's 1954 Problem List

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…

The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified…

This paper presents a framework for assigning intrinsic geometric structures to topological groups using only the data provided by their topological and algebraic structure. The geometrisation spits into small-scale and large-scale…

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on…

We give an historical account, including recent progress, on some problems of Erd\H os in number theory.

We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…

This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…

introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…

Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.

We survey the recent progress in defining open enumerative theories for Landau-Ginzburg models. We illustrate the ideas required to develop these new foundations. In particular, we describe how to define the open enumerative invariants as…

This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…

The field of ageing science has gone through remarkable progress in recent decades, yet many fundamental questions remain unanswered or unexplored. Here we present a curated list of 100 open problems in ageing and longevity science. These…

We develop new techniques in the theory of convex surfaces to prove complete classification results for tight contact structures on lens spaces, solid tori, and T^2 X I. Erratum: In this note we seek to remedy errors which appeared in…

We introduce the notion of a zebra structure on a surface, which is a more general geometric structure than a translation structure or a dilation structure that still gives a directional foliation of every slope. We are concerned with the…

We survey some results on toric topology.

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.