Papers on Algebraic Geometry over Groups

1. 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. [.pdf] [.ps]

Abstract to appear.

2. 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] [.ps]

Abstract to appear.

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

Abstract to appear.

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

Abstract to appear.

5. 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. [.pdf] [.ps]

Abstract to appear.

6. Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz (with O. Kharlampovich). Journal of Algebra 200 (1998), no. 2, 472-516. [.pdf] [.ps]

Abstract to appear.

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

Abstract to appear.

8. Dimensions and coordinate groups for a product of irreducible algebraic sets (with G. Baumslag and V. Remeslennikov). Combinatorial and computational methods in mathematics (Omsk, Russia, 1998), 24-26. [.pdf] [.ps]

Abstract to appear.

9. Two theorems about equationally Noetherian groups (with G. Baumslag and V. Roman’kov). J. of Algebra 194 (1997), no. 2, 654-664. [.pdf] [.ps]

Abstract to appear.