Bar-Natan’s geometric complex and a categorification of the Dye–Kauffman–Miyazawa polynomial
2016 ◽
Vol 25
(01)
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pp. 1550076
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In this paper, we construct a categorification of the two-variable Dye–Kauffman–Miyazawa polynomial by utilizing Bar-Natan’s construction of the Khovanov homology and homotopy quantum field theories (HQFTs) given by Turaev. In particular, for any stable equivalence class, we construct a [Formula: see text]-graded link homology over [Formula: see text] whose graded Euler characteristic is the two-variable Dye–Kauffman–Miyazawa polynomial. Moreover, we show that it is isomorphic to a special case of Dye–Kauffman–Manturov’s categorification. In this sense, we explain the special case of Dye–Kauffman–Manturov’s homology in terms of Bar-Natan’s construction.
2013 ◽
Vol 24
(10)
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pp. 1350078
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Keyword(s):
1984 ◽
Vol 25
(10)
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pp. 3076-3085
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Keyword(s):
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2020 ◽
Vol 377
(2)
◽
pp. 947-969
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1991 ◽
Vol 263
(3-4)
◽
pp. 411-416
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