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There exists a simplified Bar-Natan Khovanov complex for open 2-braids. TheKhovanov cohomology of a knot diagram made by gluing tangles of this type istherefore often amenable to calculation. We lift this idea to the level of theLipshitz-Sarkar stable homotopy type and use it to make new computations.  Similarly, there exists a simplified Khovanov-Rozansky sl_n complex for open2-braids with oppositely oriented strands and an even number of crossings.Diagrams made by gluing tangles of this type are called matched diagrams, andknots admitting matched diagrams are called bipartite knots. To a pairconsisting of a matched diagram and a choice of integer n >= 2, we associate astable homotopy type. In the case n = 2 this agrees with the Lipshitz-Sarkarstable homotopy type of the underlying knot. In the case n >= 3 the cohomologyof the stable homotopy type agrees with the sl_n Khovanov-Rozansky cohomologyof the underlying knot.  We make some consistency checks of this sl_n stable homotopy type and showthat it exhibits interesting behaviour. For example we find a CP^2 in the sl_3type for some diagram, and show that the sl_4 type can be interesting for adiagram for which the Lipshitz-Sarkar type is a wedge of Moore spaces.

An sl_n stable homotopy type for matched diagrams