The Poincare conjecture 

Page maintained by Jean-Claude Evard. Last update: June 30, 2003.

1.  Presentation of the Poincare Conjecture Millenium Problem  Link  
    with one million dollars prize offered by the Clay Mathematics Institute.
2. Official description of the Poincare Conjecture Millenium Problem  Link  
    with one million dollars prize offered by the Clay Mathematics Institute.
3. The seven Millenium Prize Problems  Link  with one million dollars prize each, 
    offered by the Clay Mathematics Institute.
4. Description of the Poincare conjecture  Link  on MathWorld, 
    by Eric Weisstein at Wolfram Research.
5. Description of Thurston's Geometrization Conjecture  Link , on MathWorld, 
    by Eric Weisstein at Wolfram Research.
6. Description of Ricci flows  Link , on MathWorld, 
    by Eric Weisstein at Wolfram Research.

 Work of Grigory Perelman on the Poincare conjecture 

April 15, 2003: There is a hope that the Poincare conjecture might be 
solved in the near future: In an article published in the Moscow Times of 
April 16, in the New York Times of April 15, and in the Seattle Post 
Intelligencer of April 15 Sara Robinson  Link  reports that Grigory Perelman, 
from the Steklov Institute of Mathematics in St. Petersburg, has announced that 
he knows how to prove the Poincare Conjecture from partial results on 
Thurston's geometrization conjecture using Ricci flows. He gave his first formal 
lectures on his work just before April 15, 2003 at the Massachusetts Institute of 
Technology, and just after this he gave another lecture series at the State 
University of New York at Stony Brook.

 Additional information: 
  1. Article of Sara Robinson in the Moscow Times of April 16:  Link .
  2. Comments  Link  of April 15, 2003, on MathWorld, Headline News, 
      by Eric Weisstein at Wolfram Research.
  3. Comments of February, 2003  Link  of John Milnor  Link  at Stony Brook University.
  4. Lecture series presented by Grigory Perelman at the Massachusetts Institute 
      of Technology from April 7, 9, and 11, 2003  Link .
  5. Lecture series presented by Grigory Perelman at Stony Brook University 
      from April 21 to May 2, 2003  Link .
  6. Papers posted by Grigory Perelman on Mathematics ArXiv:  Link .
  7. Web site of Ian Agol at the University of Illinois at Chicago:  Link .
8. Ian Agol's research blog of February 26, 2003:  Link .
9. Copy of an e-mail  Link  from Zbigniew Fiedorowicz sent on 
     November 18, 2002 to the Algebraic Topology Discussion Group 
     moderated by Donald Davis  Link  at Lehigh University.7. 
10. Copy of an e-mail  Link  from Zbigniew Fiedorowicz sent on 
      November 19, 2002 to the Algebraic Topology Discussion Group 
      moderated by Donald Davis  Link  at Lehigh University.
11. Copy of an e-mail  Link  from Grigory Perelman forwarded 
      by Vitali Kapovitch on November 20, 2002 to the Algebraic Topology 
      Discussion Group moderated by Donald Davis  Link  at Lehigh University.
12. Comments on the Young Mathematicians Network  Link  by John Vano  Link .
13. E-mail of April 1, 2003 from Tim Chow to Math Forum  Link .
14. E-mail of April 4, 2003 from Greg Kuperberg to Math Forum  Link .

 Work of Martin Dunwoody on the Poincare conjecture 

April 2002: Advance toward the proof of the Poincare Conjecture: 
A reduction of the problem of proving the Poincare conjecture has been 
posted  Link  by Martin Dunwoody  Link  at the University of 
Southampton in the United Kingdom. 
 Additional information: 
1. Update  Link  from Martin Dunwoody in the above mentioned reduction: 
    Colin Rourke has pointed out there is a problem in the statement “This 
    2-sphere will have the property that for any equivalence class {p, q} and 
    any 2- simplex sigma containing it, the arcs of C pp', qq' containing p, q 
    are uncrossed, i.e. it uncrosses every configuration.” It is certainly true for 
    any configuration as in Fig 2, but I do not see how to prove it for the Fig 3 
    ones. There may be an argument using thin position (I hope!)
2. Comments  Link  of April 9, 2002, on MathWorld, Headline News, 
    by Eric Weisstein at Wolfram Research.
3. Puzzler Solved, Topology and the Million Dollars Poincare 
    Conjecture  Link , by John Allen Paulos at the Temple University, 
    for ABCNews, May 5, 2002.
4. British professor chases solution to one million dollar mathematics 
    prize  Link , by Robert Matthews, science correspondent 
    at Hollinger Telegraph New Media  Link , April 14, 2002. 
5. Determining whether Poincare conjecture is true or false is one of the seven 
    Millennium Prize Problems  Link  with a prize of one million dollars each, 
    organized by the Clay Mathematics Institute  Link .  
6. See John Baez's description of the seven Millennium Prize Problems  Link . 
7. A workshop  Link  entitled "Topology in and around dimension three", 
    organized by the Pacific Institute for Mathematical Sciences  Link , 
    and by the Mathematical Sciences Research Institute  Link   
    will be held at Banff International Research Station  Link   
    in September 13-18, 2003.

 Work of Sergey Nikitin on the Poincare conjecture 

December 10, 2002: A revised version of a submitted proof of the Poincare 
conjecture is posted on the internet by Sergey Nikitin at Arizona State University.
Additional information:
  1. Web sites of Sergey Nikitin  Link  and  Link .
  2. October 23 to November 27, 2002: Discussion of the previous versions 
      of his paper on Math Forum  Link .
  3. October 23, 2002: E-mail from Michael Anshel to Math Forum  Link .
  4. October 25, 2002: Copy of an e-mail  Link  from Krzysztof Pawalowski 
      sent to the Algebraic Topology Discussion Group 
      moderated by Donald Davis  Link  at Lehigh University.7. 
  5. October 26, 2002: Copy of an e-mail  Link  from Vitali Kapovitch 
      sent to the Algebraic Topology Discussion Group 
      moderated by Donald Davis  Link  at Lehigh University.7. 
  6. October 30, 2002, 13:41:14 GMT: E-mail from Larry Hammick to Math Forum  Link .
  7. October 30, 2002, 17:40:40 GMT: E-mail from Ignat Soroko to Math Forum  Link .
  8. October 30, 2002, 20:44:10 GMT: E-mail from Lee Rudolph to Math Forum  Link .
  9. October 31, 2002, 04:41:20 GMT: E-mail from David Johnson to Math Forum  Link .
10. October 31, 2002, 17:27:06 GMT: E-mail from Christophe Margerin to Math Forum  Link .
11. November 4, 2002: Copy of an e-mail  Link  from Krzysztof Pawalowski 
      sent to the Algebraic Topology Discussion Group 
      moderated by Donald Davis  Link  at Lehigh University.7. 
12. November 18, 2002: E-mail from Ian Ferris to Math Forum  Link .
13. November 27, 2002: E-mail from Chan-Ho Suh to Math Forum  Link .
14. December 10, 2002: Copy of the eighth version of his paper  Link ,
      posted on his Web site.
15. December 10, 2002: Comments from Sergey Nikitin on the 
      eight successive versions of his paper  Link  posted on the Web site ArXiv.

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