my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
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Outline<br />
Definitions and examples<br />
Homological properties of kC-mod<br />
An example<br />
Finite categories and their algebras<br />
Re<strong>presentation</strong>s and modules<br />
Motivation<br />
A proper setting for ordinary cohomology<br />
The natural functor π : G ⋉ P → G induces a ring<br />
homomorphism, the restriction,<br />
H ∗ (G; k) → H ∗ (G ⋉ P; k).<br />
Becker and Gottlieb constructed a transfer map<br />
H ∗ (G ⋉ P; k) → H ∗ (G; k) such that tr ◦ res = χ(P), the<br />
Euler characteristic of P.<br />
Applying a spectral sequence to P ↩→ G ⋉ P → G one<br />
can show H ∗ (G ⋉ P; k) is a finitely generated<br />
H ∗ (G; k)-module, and hence is finitely generated as a<br />
ring.<br />
Fei Xu<br />
Finite category algebras