Colored torus links are parity

Let b=(b1,,bm){\bm{b}}=(b_1,\ldots,b_m) and let T(m,m;b)T(m,m;{\bm{b}}) be the b{\bm{b}}-colored (m,m)(m,m)-torus link. Colored torus-link parity conjecture. The link T(m,m;b)T(m,m;{\bm{b}}) is parity; more generally, every colored positive torus link is parity. The uncolored positive torus-link case is known, but the colored generalization remains open.

Sources & referencesView supporting material

Primary source

Matthew Hogancamp, David E. V. Rose and Paul Wedrich, “Link splitting deformation of colored Khovanov–Rozansky homology”, arXiv:2107.09590 (2021).

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