**Definitions**: Recall that we let , and defined a bilinear form on by .

A linear map is a Lorentz transformation if for any , we have . 450 more words

**Definitions**: Recall that we let , and defined a bilinear form on by .

A linear map is a Lorentz transformation if for any , we have . 450 more words

Let be the diagonal matrix . We can use to define a bilinear form on namely, for Define the norm square . Let

1). A vector is space-like if , light-like if , and time-like if . 73 more words

It’s been a while since I last blogged; the reason, of course, is that I felt that I couldn’t post anything new before completing my series of posts on Kähler groups; but I wasn’t quite ready to write my last post, because I wanted to get to the bottom of a few analytic details in the notorious Gromov-Schoen paper. 357 more words

Marc Culler and I released SnapPy 2.1 today. The main new feature is the ManifoldHP variant of Manifold which does all floating-point calculations in quad-double precision… 202 more words