rybu's blog

One of the things I find pretty neat about the splicing operad is how much goes into it. It's a relatively complicated structure and I'm a little surprised there aren't many similar, related structures in the literature.

Shortly after arriving as a postdoc at the University of Rochester I started getting results on the global topology of spaces of knots. This was, in a sense, the first topic I had wanted to work on for my dissertation. But I got stuck, and my Ph.D evolved to a different topic. At Rochester, sparked by Fred Cohen's curiosity, the project regained momentum.

One afternoon I was sitting around with Paolo Salvatore, trying to prove that an operad of little cubes had no hope of acting on spaces of string links. I was certain the operad couldn't act and kept on insisting on it. Eventually Paolo came up with a proof. This post is about Paolo's idea.

My take, written up here.

Towards the end of June the University of Brisbane is hosting a conference on a subject which as the quote above suggests, is something of a barren landscape scattered with unsavory characters.

IPMU (the Institute for the Physics and Mathematics of the Universe) officially opened its new building this week. Ben Burton and I were in Tokyo visiting and I took some photos.

Back when I was a grad student, the Lawrence-Krammer representations of the braid groups were a relatively new thing.

The creative process for papers has always been murky to me. I rarely set out to write a particular type of paper. Quite often results appear as by-products of computations I'm working on for some other reason.

Some nice news -- Antoni Kosinski's Differential Manifolds book has been Dovered. The review on Amazon is pretty honest in that it's a book that's not without its problems. I don't know if it's me, but that just makes the book more readable. I've always had trouble reading Milnor's books because there aren't enough errors to keep me entertained. I like books to present the big idea, give me a few clues and then let me work out the details.

There's a fair amount of papers in the literature on the homotopy and homology of spaces of knots. An oddity that probably isn't apparent to the casual reader is that very little is known about torsion in the homology of knot spaces. To be precise, let's `normalize' this discussion and consider knot spaces to be the space smooth of embeddings of R^j in Rⁿ which agree with a fixed linear embedding outside of a fixed ball.