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math.AT2023
Cubes, cacti, and framed long knots
Robin Koytcheff, Yongheng Zhang
We define an action of the operad of projective spineless cacti on each stage of the Taylor tower for the space of framed 1-dimensional long knots in any Euclidean space. By mappin…
math.AT2016★ 5 cited
Permutahedral Structures of Operads
Ralph M. Kaufmann, Yongheng Zhang
There are basically two interesting breeds of operads, those that detect loop spaces and those that solve Deligne's conjecture. The former deformation retract to Milgram's sp…
math.AT2015
Lusternik-Schnirelmann category and based topological complexities of motion planning
Yongheng Zhang
Farber and Rudyak introduced topological complexity of motion planning and its higher analogs to measure the complexity of assigning paths to po…