Originating from the German word “klasse” (class), both topological and algebraic K-theory operates
under the philosophy that studying certain isomorphism classes of objects over a space/ scheme/ ring/
category is a good way to study that space (/scheme/ ring / category). In the case of topological K-theory,
we’ll consider isomorphism classes of vector bundles over a space X, whereas in algebraic
K-theory we’ll look at finitely generated projective modules over a ring R. The Serre-Swan theorem will allow
us to reconcile these stories on the level of K_0. We’ll finish the talk with an algebraic description of K_1(R)
and K_2(R), as well as Quillen’s “+” construction for defining higher algebraic K-groups.
under the philosophy that studying certain isomorphism classes of objects over a space/ scheme/ ring/
category is a good way to study that space (/scheme/ ring / category). In the case of topological K-theory,
we’ll consider isomorphism classes of vector bundles over a space X, whereas in algebraic
K-theory we’ll look at finitely generated projective modules over a ring R. The Serre-Swan theorem will allow
us to reconcile these stories on the level of K_0. We’ll finish the talk with an algebraic description of K_1(R)
and K_2(R), as well as Quillen’s “+” construction for defining higher algebraic K-groups.
| Building: | East Hall |
|---|---|
| Event Type: | Workshop / Seminar |
| Tags: | Mathematics |
| Source: | Happening @ Michigan from Student Commutative Algebra Seminar - Department of Mathematics, Department of Mathematics |
