TY - JOUR
T1 - Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism
AU - Hamilton, Alastair
PY - 2013/8/20
Y1 - 2013/8/20
N2 - Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how evaluating these cohomology classes upon a well-known construction producing homology classes in the moduli space can be expressed in terms of the Feynman diagram expansion of some functional integral. By computing these integrals for specific examples, we are able to demonstrate that this construction produces families of nontrivial classes.
AB - Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how evaluating these cohomology classes upon a well-known construction producing homology classes in the moduli space can be expressed in terms of the Feynman diagram expansion of some functional integral. By computing these integrals for specific examples, we are able to demonstrate that this construction produces families of nontrivial classes.
KW - Batalin-Vilkovisky formalism
KW - Lie algebra cohomology
KW - Moduli space of curves
KW - Noncommutative geometry
KW - Topological field theory
UR - http://www.scopus.com/inward/record.url?scp=84877887734&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2013.04.015
DO - 10.1016/j.aim.2013.04.015
M3 - Article
AN - SCOPUS:84877887734
SN - 0001-8708
VL - 243
SP - 67
EP - 101
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -