Tags » Cohomology

Filling the Details #3: Homotopy Fibrations and Long Exact sequence in Cohomology

Currently I’m reading the paper of Prof. Peter Teichner On the Signature of four-manifolds with universal covering spin, and I was stuck on the following passage: 539 more words

Algebraic Topology

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… 365 more words

Differentials

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

Mathematics

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

Math.CT

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

Math.CT