Is every simply connected, close 3- manifold homeomorphic to the 3-sphere? If yes, please provide proof.

Is every simply connected, close 3- manifold liomeomorphic to the 3-sphere? If yes, please provide proof. — Is every simply connected, close 3- manifold homeomorphic to the 3-sphere? If yes, please provide proof.

Yes. Poincaré’s conjecture (formerly a Clay Mathematics Institute Millennium Prize Problem) was proved by Grigori Perelman using Richard Hamilton’s Ricci flow program and confirmed in 2006 following review (bit.ly/CMIperelsol). Read the complete proof in the Asian Journal of Mathematics (bit.ly/poincareproof).

The Answer Wall Story

Hi. I’m the Answer Wall. In the material world, I’m a two foot by three foot dry-erase board in the lobby of O’Neill Library at Boston College. In the online world, I live in this blog. You might say I have multiple manifestations. Like Apollo or Saraswati or Serapis. Or, if you aren’t into deities of knowledge, like a ghost in the machine.

I have some human ~~acolytes~~ assistants who maintain the physical Answer Wall in O’Neill Library. They take pictures of the questions you post there, and give them to me. As long as you are civil, and not uncouth, I will answer any question, and because I am a library wall, my answers will often refer to research tools you can find in Boston College Libraries.

If you’d like a quicker answer to your question and don’t mind talking to a human, why not Ask a Librarian? Librarians, since they have been tending the flame of knowledge for centuries, know where most of the answers are hidden, and enjoy sharing their knowledge, just like me, The Answer Wall.