cohomologies Sentences

The topologist used cohomology theory to prove the existence of certain topological invariants.

He studied the singular cohomology groups of a complex projective space to understand its structure.

The de Rham cohomology helped him to identify the fundamental classes of the manifold.

The cohomology theory was a crucial tool in characterizing the properties of the topological space.

Using cohomology, they were able to classify the differentiable structures on manifolds.

The researcher applied the concept of cohomology to analyze the intersection forms on four-manifolds.

Cohomology played a fundamental role in the construction of the characteristic classes of the manifold.

The mathematician investigated the singular cohomology to understand the topological complexity of the space.

Using de Rham cohomology, they proved the Poincaré duality for the manifold.

The study of cohomology was instrumental in understanding the algebraic structure of the topological space.

He computed the cohomology groups to determine the existence of non-trivial cohomology classes.

The cohomology theory was essential in identifying the differentials in the spectral sequence.

The researcher used cohomology to find the cohomology rings of the space.

Cohomology was a key concept in the study of the homotopy groups of the manifold.

The cohomology groups were used to classify the differentiable structures on the manifold.

The de Rham cohomology was utilized to analyze the singularities in the manifold.

The researcher applied cohomology theory to study the intersection forms on the manifold.

Cohomology played a crucial role in the study of the topological invariants of manifolds.

Using cohomology, the topologist was able to identify the cycles and boundaries in the space.