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arXiv · 2505.02755

SU(3) instanton homology for webs and foams

Peter B. Kronheimer·Tomasz S. Mrowka
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Abstract

An instanton homology is constructed for webs and foams, using gauge theory with structure group SU(3), adapting previous work of the authors for the SO(3) case. Skein exact triangles are established, and using an eigenspace decomposition arising from operators associated to the edges, it is shown that the dimension of the SU(3) homology counts Tait colorings when the web is planar. Unlike the SO(3) case, the SU(3) homology is mod-2 graded. Its Euler characteristic can be interpreted as a signed count of Tait colorings, or equivalently as the value at 1 of the Yamada polynomial invariant. Some examples and variants of the construction are also discussed.

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Peter B. Kronheimer, Tomasz S. Mrowka. 2025-05-05. SU(3) instanton homology for webs and foams. https://arxiv.org/abs/2505.02755

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