Manifolds Done Right -- Bhargav Bhatt, November 29, 2004
<p>Despite the title, this talk is a rather thinly veiled introduction to
sheaves. In particular, I will motivate the definition of presheaves
and sheaves based on the examples of compact Hausdorff spaces and
differentiable manifolds. Once this is achieved, I will give the
elegant sheaf theoretic definition of a topological/differentiable/smooth/complex manifold. Time permitting, I will also
show how this definition allows us to define geometric objects like
tangent spaces intrinsically.<br>
<br>
To understand most of the talk, knowledge of basic point-set topology
and (modern) algebra is sufficient. In particular, prior familiarity
with manifolds is not necessary to follow the talk.</p>