Papers on Tarski Problems

 

1.      Isomorphism problem for finitely generated fully residually free groups (with I. Bumagin and O. Kharlampovich), submitted.[.pdf]

 

2.      Effective JSJ decompositions (with O.Kharlampovich), Contemp. Math., 378,  Amer. Math. Soc., Providence,RI, 2005, 87-212. [.pdf]

 

3.      Algebraic geometry over free groups: lifting solutions into generic points (with O. Kharlampovich), Contemp. Math., 378,  Amer. Math. Soc., Providence, RI, 2005, 213-318. [.pdf]

     

4.      Implicit function theorems over free groups (with O.Kharlampovich). J. of Algebra, 290 (2005), no. 1, 1-203. [.pdf]

 

5.      Implicit function theorem over free groups and genus problem (with O. Kharlampovich). Knots, braids, and mapping class groups---papers dedicated to Joan S. Birman (New York, 1998), 77-83, AMS/IP Stud. Adv. Math., 24, Amer. Math. Soc., Providence, RI, 2001.

 

6.      Algebraic geometry over groups III: Elements of model theory (with A.Kvaschuk and V. Remeslennikov). J. of Algebra, 288 (2005), no. 1, 78-98. [.pdf]

 

7.      Algebraic geometry 2: logical foundations (with V. Remeslennikov). J. of Algebra 234 (2000),  225-276. [.pdf]

   

8.      Algebraic geometry over groups (with G. Baumslag and V. Remeslennikov). Algorithmic problems in groups and semigroups (Lincoln, NE, 1998), 35-50, Trends Math., Birkhäuser  Boston, Boston, MA, 2000. [.pdf]

 

9.      Algebraic geometry over groups I. Algebraic sets and ideal theory (with G. Baumslag and V. Remeslennikov). J. of Algebra 219 (1999), 16-79. [.pdf]

     

10.  Description of fully residually free groups and irreducible affine varieties over a free group (with O. Kharlampovich). Summer School in Group Theory in Banff, 1996, 71-80,  CRM Proc. Lecture Notes, 17, Amer. Math. Soc., Providence, RI, 1999.

     

11.  A classification of  fully residually free groups of rank three or less (with A. Gaglione, B. Fine, G. Rosenberger and D.Spellman). J. of Algebra, 200 (1998), no. 2, 571-605.

     

12.  Irreducible affine varieties over a free group. II:  Systems in triangular quasi-quadratic form and description of residually free groups (with O. Kharlampovich). J. of Algebra 200 (1998), no. 2, 517--570. [.pdf]