论文标题
ozsvath-szabo的边界HFK的兼容性通过更高的表示形式
Compatibility in Ozsvath-Szabo's bordered HFK via higher representations
论文作者
论文摘要
我们在Ozsváth-Szabó的“边界浮子同源性”理论中配备了本地交叉双模型，并具有1个2-陈述的1型晶状体的结构，对$ u_q（\ mathfrak {gl}（gl}（1 | 1 | 1 | 1）^+）^+ - ^+）$ - - - - - 1 | 1）除了与Rouquier和第二作者的作品一致的边界的平面同源性和更高代表理论之间产生新的联系外，该结构还对Ozsváth-Szabó'sBimodules的``Summands'属性''之间的``兼容性''进行了代数重新制定，这在从本地交叉构建其从本地交叉上到更全球的Tangles Tangles and Global Global Global Tangles and Knots和Kneots of toozsváthsbimodules'''''''''''。
We equip the basic local crossing bimodules in Ozsváth-Szabó's theory of bordered knot Floer homology with the structure of 1-morphisms of 2-representations, categorifying the $U_q(\mathfrak{gl}(1|1)^+)$-intertwining property of the corresponding maps between ordinary representations. Besides yielding a new connection between bordered knot Floer homology and higher representation theory in line with work of Rouquier and the second author, this structure gives an algebraic reformulation of a ``compatibility between summands'' property for Ozsváth-Szabó's bimodules that is important when building their theory up from local crossings to more global tangles and knots.
