Related papers: On flag-no-square $4$-manifolds
In this note we show that there are 4-manifolds not containing Gompf nucleus $N_2$; in this way we answer Problem 4.98 of Kirby's problem list in the negative.
The main result of this paper is an expression of the flag curvature of a submanifold of a Randers-Minkowski space $({\mathscr V},F)$ in terms of invariants related to its Zermelo data $(h,W)$. More precisely, these invariants are the…
We prove that every smoothly embedded surface in a 4--manifold can be isotoped to be in bridge position with respect to a given trisection of the ambient 4--manifold; that is, after isotopy, the surface meets components of the trisection in…
We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that the connected sum M # N admits a conformally flat Riemannian metric.
We prove that among all flag 3-manifolds on $n$ vertices, the join of two circles with $\left\lceil{\frac{n}{2}}\right \rceil$ and $\left\lfloor{\frac{n}{2}}\right \rfloor$ vertices respectively is the unique maximizer of the face numbers.…
Some aspects of the construction of SW Floer homology for manifolds with non-trivial rational homology are analyzed. In particular, the case of manifolds that are obtained as zero-surgery on a knot in a homology sphere, and for torsion…
The octonionic flag manifold $Fl(\mathbb{O})$ is the space of all pairs in $\mathbb{O}P^2\times \mathbb{O}P^2$ (where $\mathbb{O}P^2$ denotes the octonionic projective plane) which satisfy a certain "incidence" relation. It comes equipped…
Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling construction to 2-complexes over certain finite abelian groups…
BPS lumps in ${\cal N}=2$ SUSY nonlinear sigma models on hyper-\kahler manifolds in four dimensions are studied. We present new lump solutions with various kinds of topological charges. New BPS equations and a new BPS bound, expressed by…
It is known that there are four-manifolds which are not algorithmically recognizable. This implies that there exist triangulations of these manifolds which are separated by large barriers from the point of view of the computer algorithm. We…
We prove a noncommutative analogue of Minkowski's integral inequality for commuting squares of tracial von Neumann algebras. The inequality implies a necessary condition for a quadruple of graphs to be realized as inclusion graphs of a…
The famous Haken-Kneser-Milnor theorem states that every 3-manifold can be expressed in a unique way as a connected sum of prime 3-manifolds. The analogous statement for 3-orbifolds has been part of the folklore for several years, and it…
Using the formalism of flag algebras, we prove that every triangle-free graph $G$ with $n$ vertices contains at most $(n/5)^5$ cycles of length five. Moreover, the equality is attained only when $n$ is divisible by five and $G$ is the…
Fintushel and Stern have proved that if S \subset X is a symplectic surface in a symplectic 4-manifold such that S has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent…
We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a…
We classify edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^4b$ and with any irrational angle in degree: they are three $1$-parameter families of pentagonal subdivisions of the Platonic solids, with…
For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$, $\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and…
Many three dimensional manifolds are two-fold branched covers of the three dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and many examples. It shows that there are…
It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…
Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing…