mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold. It reflects...

modeled as a pseudo-Riemannian 4-manifold. The homotopy type of a simply connected compact 4-manifold only depends on the intersection form on the middle...

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional...

algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties,...

Boca Raton, Florida, 2002. 4-manifold 5-manifold Casson handle Exotic R4 Fake 4-ball Intersection form of a 4-manifold Möbius energy Wikimedia Commons...

low-dimensional topology, a branch of mathematics, the E8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the E8 lattice...

In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (or...

quantum intersection rings, Gromov–Witten theory and the extension of intersection theory from schemes to stacks. For a connected oriented manifold M {\displaystyle...

a subject of mathematics, a symplectic manifold is a smooth manifold, M {\displaystyle M} , equipped with a closed nondegenerate differential 2-form ω...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form is positive...

a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic...

it is a usual axiom of a manifold to be a Hausdorff space. In general topology, this axiom is relaxed, and one studies non-Hausdorff manifolds: spaces...

is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given a Riemannian...

intersection homology groups. The intersection homology groups are independent of the choice of stratification of X. If X is a topological manifold,...

mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface...

a complex K3 surface, which has signature 3−19 = −16. The conjecture would imply that every simply connected smooth 4-manifold with even intersection...

methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. A generalization...

used by Simon Donaldson to prove facts about the intersection form of simply connected 4-manifolds. In some cases techniques from contemporary physics...

In mathematics, a pseudomanifold is a special type of topological space. It looks like a manifold at most of its points, but it may contain singularities...

In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as...

a smooth manifold has diagonalisable intersection form. The moduli space of ASD instantons may be used to define further invariants of four-manifolds...

second fundamental form), differential topology (intersection forms of manifolds, especially four-manifolds), Lie theory (the Killing form), and statistics...

the context of automorphic forms in the 1950s under the name V-manifold; by William Thurston in the context of the geometry of 3-manifolds in the 1970s...

define an invariant of (4k + 2)-dimensional manifolds (singly even-dimensional manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain...

generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight...

founded intersection theory of cycles on manifolds. On a closed oriented n-dimensional manifold M an i-cycle and a j-cycle with nonempty intersection will...

independently proven that any such manifold admits a parallel 4-form Ω {\displaystyle \Omega } .The long-awaited analog of strong Lefschetz theorem was published...

theorem (Donaldson 1983a, 1983b, 1987a): If the intersection form of a smooth, closed, simply connected 4-manifold is positive- or negative-definite then it...

loop space of a symplectic manifold with the symplectic action functional. For the (instanton) version for three-manifolds, it is the space of SU(2)-connections...