Several months ago a paper was posted at
<http://arxiv.org/abs/1001.4164>
called "Another way of answering Henri Poincaré's fundamental question." The author gave a talk on it today at my institution. If it's correct, it is a major breakthrough in terms of proof length (~10 pages). However, it is very outside my specialty. There's apparently been very little feedback, but the author is ok with public discussion. Therefore, can anyone say whether they have read the paper? Whether it is correct, missing details, clearly flawed, or what have you?



Does this approach for the Poincaré conjecture work?
I had a quick look. Although I haven't found a specific error, as far as I can tell, he's not using the hypothesis of simple-connectivity anywhere in an essential way. Even though he posits this as a hypothesis in Prop. 5.6, the proof of this proposition works for any manifold with 2-sphere boundary (also, Prop. 4.4 works for any homology ball). Thus, in Step (4) of his proof of Prop. 5.8, when he refers to Prop. 5.6, this step is not making essential use of simple-connectivity. 


