# nLab Alex Hoffnung

chains. Here we will sketch the idea and eventually should formalize this on the page for Borel-Moore homology. In the meantime the Wikipedia article plus its references and the Chriss-Ginzburg book Representation Theory and Complex Geometry provide plenty of information.

$H_\bullet(Y) = (possibly\; unbounded)\; i-chains\; in\; Y\;(with\; coefficients\; in \;\mathbb{C})$
$H_i(Y) = i-dim\; subspace\;of\; Y \;without\; boundary \;(possibly \;singular\; or\; unbounded)$

The construction starts by triangulating the space and considering the vector space of formal sums of $i$-simplices.

Of course, one wants independence of triangulation so we need to take a direct limit of these vectors spaces over all refinements of the triangulation. The boundary map then comes from simplicial homology and we have a chain complex. The homology of this complex is the Borel-Moore homology.

Alex

Other projects:

1) Understand q-Schur algebras and relationship to representation theory of Hecke algebras

2) Learn lots of things in Ginzburg-Chriss.

3) Write my thesis!

4) Write everything else I should be writing.

5) Get a job! :)

I guess 3) and 5) are taken care of now.

If anyone wants to talk about the first item that would be great. I guess this is my new recruiting station to get people to talk to me about math.

category: people

Last revised on March 17, 2021 at 17:34:37. See the history of this page for a list of all contributions to it.