Related papers: Characteristic Topological Invariants
Gromov-Witten invariants of a symplectic manifold are a count of holomorphic curves. We describe a formula expressing the GW invariants of a symplectic sum $X# Y$ in terms of the relative GW invariants of $X$ and $Y$. This formula has…
We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial…
We prove that the Green--Griffiths--Demailly (GGD) hyperbolicity thresholds are structurally invariant. In other words, the minimal jet order and asymptotic growth rate at which invariant jet differentials appear remain unchanged when…
For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…
The Euler characteristic, thought of as a function that assigns a numerical value to every finite simplicial complex, is locally determined in both a combinatorial sense and a geometric sense. In this note we show that not every function…
Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies…
For a finitely presented discrete group $\Gamma$, we introduce two generalizations of the orbifold Euler characteristic and $\Gamma$-orbifold Euler characteristic to a class of proper topological groupoids large enough to include all…
Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…
For a graph $G=(V,E)$, and a symplectic vector space $(W, \left<\cdot,\cdot\right>)$, we define a variety $X(G,W)$ consisting of all functions $w:V\to W$ satisfying $\left<w(u), w(v)\right> = 0$ for any edge $\{u,v\}$ in $G$. We study the…
For any connected component $H_0$ of the space of real meromorphic functions we build a compactification $N(H_0)$ of the space $H_0$. Then we express the Euler characteristics of the spaces $H_0$ and $N(H_0)$ in terms of topological…
The {\em abstract boundary\/} (or {\em {\em a\/}-boundary\/}) of Scott and Szekeres \cite{Scott94} constitutes a ``boundary'' to any $n$-dimensional, paracompact, connected, Hausdorff, $C^\infty$-manifold (without a boundary in the usual…
The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much…
The notion of the orbifold Euler characteristic came from physics at the end of 80's. There were defined higher order versions of the orbifold Euler characteristic and generalized ("motivic") versions of them. In a previous paper the…
The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres and closed manifolds: if a set $X$ is homeomorphic to a sphere or a closed manifold, then any…
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the…
The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…
Characterizing face-number-related invariants of a given class of simplicial complexes has been a central topic in combinatorial topology. In this regard, one of the well-known invariants is $g_2$. Let $K$ be a normal $3$-pseudomanifold…
In a previous paper the authors elaborated notions and technique which could be applied to compute such invariants of polynomials as Euler characteristics of fibres and zeta-functions of monodromy transformations associated with a…
A finite abstract simplicial complex G defines a matrix L, where L(x,y)=1 if two simplicies x,y in G intersect and where L(x,y)=0 if they don't. This matrix is always unimodular so that the inverse g of L has integer entries g(x,y). In…