# Tagged Questions

**1**

vote

**0**answers

85 views

### Distributing the Hodge map over the wedge product

Let $(V,\langle,\rangle)$ be a finite dimensional inner product space, $V^{\wedge}$ it exterior algebra, and $\ast$ the Hodge star arising from $\langle,\rangle$. Does there exist any formula to ...

**0**

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**0**answers

251 views

### Why does the Lefschetz Operator not Square to Zero?

I'm trying to learn about the Lefschetz decomposition but am having a very basic problem: For the fundamental form $K$ of a Kahler metric on a complex manifold $M$, the corresponding Lefschetz ...

**26**

votes

**11**answers

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### Why is the exterior algebra so ubiquitous?

The exterior algebra of a vector space V seems to appear all over the place, such as in
the definition of the cross product and determinant,
the description of the Grassmannian as a variety,
the ...