Wedge sum

With the wedge product (after wedge eng wedge;. Well Einpunktvereinigung or bouquet called ) of two dotted topological spaces and referred to their disjoint union, which is glued ( the base point ) at one point. Formally, the definition is as follows:

Herein, the respective base point.

The construction can also be generalized to an arbitrary number of rooms:

Abstract can understand the wedge product as the coproduct in the category of topological spaces dotted.

Role in algebraic topology

The wedge product behaves well with respect to some functors in algebraic topology. For example applies to the fundamental group of locally contractible spaces

The free product of the groups referred to.

In the singular homology applies:

You can embed the wedge product in an obvious way into the product, the quotient

Is the smash product.

In particular, the reduced device to attach, of importance in the stable homotopy theory.

The wedge product is also used in the definition of the link in the homotopy groups.

• Topology