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

VL - 243

SP - 67

EP - 101

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -