The Gram determinant of type A was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type A by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determinant. We conclude the paper by discussing Chen's conjecture about the Gram determinant of type Mb evaluated in the Klein bottle.

中文翻译：

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类型A的Gram行列式的推广

Lickorish在其关于3-流形不变量的工作中引入了类型A的革兰氏行列式。我们通过在圆环中评估圆盘中非相交连接的双线性形式来概括A型革兰氏行列式的理论。主要结果为该革兰氏决定因素提供了一个封闭式。通过讨论Chen关于在Klein瓶中评估的Mb型革兰氏决定因素的猜想来结束本文。