Geodesic
Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 26-44

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the Lie algebra $L_1$ of formal vector fields on the line which vanish at the origin together with their first derivatives. V. M. Buchstaber and A. V. Shokurov showed that the universal enveloping algebra $U(L_1)$ is isomorphic to the Landweber–Novikov algebra $S$ tensored \with the reals. The cohomology $H^*(L_1)=H^*(U(L_1))$ was originally calculated by L. V. Goncharova. It follows from her computations that the multiplication in the cohomology $H^*(L_1)$ is trivial. Buchstaber conjectured that the cohomology $H^*(L_1)$ is generated with respect to nontrivial Massey products by one-dimensional cocycles. B. L. Feigin, D. B. Fuchs, and V. S. Retakh found a representation for additive generators of $H^*(L_1)$ in the desired form, but the Massey products indicated by them later proved to contain the zero element. In the present paper, we prove that $H^*(L_1)$ is recurrently generated with respect to nontrivial Massey products by two one-dimensional cocycles in $H^1(L_1)$.
Keywords: Massey product, graded Lie algebra, formal connection, representation, cohomology.
Mots-clés : Maurer–Cartan equation 
@article{FAA_2009_43_4_a3,
     author = {D. V. Millionshchikov},
     title = {Algebra of {Formal} {Vector} {Fields} on the {Line} and {Buchstaber's} {Conjecture}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {26--44},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a3/}
}
TY  - JOUR
AU  - D. V. Millionshchikov
TI  - Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2009
SP  - 26
EP  - 44
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a3/
LA  - ru
ID  - FAA_2009_43_4_a3
ER  - 
%0 Journal Article
%A D. V. Millionshchikov
%T Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2009
%P 26-44
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a3/
%G ru
%F FAA_2009_43_4_a3
D. V. Millionshchikov. Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 26-44. http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a3/