Exact triangles for SO(3) instanton homology of webs
Exact triangles for SO(3) instanton homology of webs
复制标题
SO(3) 网瞬时同源性的精确三角形
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
T. Mrowka
中科院分区：
文献类型：
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作者：
P. Kronheimer;T. Mrowka
作者最近引入的SO(3)瞬子同调将两个元素域上的有限维向量空间与每个嵌入的三价图（或“网”）联系起来。本文建立了这种瞬子同调的绞合精确三角形，并实现了八面体公理。从八面体图中，我们可以推导出作者猜想的等价重新表述：对于平面网，瞬子同调的秩等于Tait着色的个数。
The SO(3) instanton homology recently introduced by the authors associates a finite‐dimensional vector space over the field of two elements to every embedded trivalent graph (or “web”). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings.