Tags » Cohomology

The Gelfand-Fuchs cocycle

Let be a vector field on the Euclidean line . Expressed in a coordinate the vector field is . The logarithm of the component value at each point of the vector field is the fundamental Euclidean invariant… 363 more words


Random Exercise #2: Problem 11-C in Milnor's Characteristic Classes

Todays’ random exercise will be the pretty famous exercise 11-C  one can find in Milnor’s Book. Let me recall the statement:

Let and be compact oriented manifolds with smooth embedding . 393 more words

Algebraic Topology

Random Exercise #1 "Isomorphism in cohomology induces Isomorphism in Homology"

I’ve decided to start collecting here some random exercises arose during discussions with my colleagues (usually during the weekly pizza-time) and I found interesting.

Let be a continuous map between topological spaces, and some coefficients. 293 more words

Algebraic Topology

impossible objects

Recently in between studying for my finals I’ve been learning about a whole load of different things in algebraic geometry, a main one being cohomology… 733 more words


Forms and Galois cohomology

Yesterday we gave a brief and abstract description of Galois descent, the punchline of which was that Galois descent could abstractly be described as a natural equivalence… 1,352 more words


Projective representations are homotopy fixed points

Yesterday we described how a (finite-dimensional) projective representation of a group functorially gives rise to a -linear action of on such that the Schur class classifies this action. 870 more words


Projective representations give categorical representations

Today we’ll resolve half the puzzle of why the cohomology group appears both when classifying projective representations of a group over a field and when classifying -linear actions of on the category of -vector spaces by describing a functor from the former to the latter. 898 more words