The age grading and the Chen-Ruan cup product

TY - JOUR

T1 - The age grading and the Chen-Ruan cup product

AU - A. Hepworth, Richard

N1 - Keywords: math.AT; math.AG

PY - 2010/10

Y1 - 2010/10

N2 - We prove that the obstruction bundle used to define the cup-product in Chen-Ruan cohomology has a simple representation-theoretic description. The key quantities in this description are the age gradings or degree-shifting numbers of the representations of the local groups of the orbifold. We obtain a Künneth Theorem for Chen-Ruan cohomology as a direct consequence of an elementary property of the age grading, and explain how several other results, including associativity of the cup product, can be proved in a similar way.

AB - We prove that the obstruction bundle used to define the cup-product in Chen-Ruan cohomology has a simple representation-theoretic description. The key quantities in this description are the age gradings or degree-shifting numbers of the representations of the local groups of the orbifold. We obtain a Künneth Theorem for Chen-Ruan cohomology as a direct consequence of an elementary property of the age grading, and explain how several other results, including associativity of the cup product, can be proved in a similar way.

U2 - 10.1112/blms/bdq043

DO - 10.1112/blms/bdq043

M3 - Journal article

SN - 0024-6093

VL - 42

SP - 868

EP - 878

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 5

ER -