THE MODULI PROBLEM OF LOBB AND ZENTNER AND THE COLORED ??(N) GRAPH INVARIANT
THE MODULI PROBLEM OF LOBB AND ZENTNER AND THE COLORED ??(N) GRAPH INVARIANT
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洛布和齐特纳的模问题及彩色??(N)图不变量
DOI：
10.1142/s0218216513500600
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发表时间：
2012
影响因子：
0.5
通讯作者：
Jonathan Grant
中科院分区：
文献类型：
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作者：
Jonathan Grant
受 Kronheimer 和 Mrowka 的 SU(N) 瞬时结弗洛尔同调与 ??(N) Khovanov-Rozansky 同调之间可能存在的联系的启发，Lobb 和 Zentner 最近引入了一个与三价图着色相关的模问题，村上、Ohtsuki 和 Yamada 在量子 ??(N) 结多项式的状态和解释中考虑了这种问题。对于具有两种颜色的图，他们表明该模空间可以被认为是一种表示簇，并且其欧拉特征等于在 1 处评估的图的 ??(N) 多项式。我们通过 ??(N) 的不可约反对称表示将他们的结果扩展到具有任意着色的图。
Motivated by a possible connection between the SU(N) instanton knot Floer homology of Kronheimer and Mrowka and ??(N) Khovanov–Rozansky homology, Lobb and Zentner recently introduced a moduli problem associated to colorings of trivalent graphs of the kind considered by Murakami, Ohtsuki and Yamada in their state-sum interpretation of the quantum ??(N) knot polynomial. For graphs with two colors, they showed this moduli space can be thought of as a representation variety, and that its Euler characteristic is equal to the ??(N) polynomial of the graph evaluated at 1. We extend their results to graphs with arbitrary colorings by irreducible anti-symmetric representations of ??(N).