Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop (g =2, 3) graphs

In this paper, we give some non-trivial geometric cycles of the space of long embeddings R^j --> R^n (n-j >= 2) modulo immersions. We construct a class of cycles from specific chord diagrams associated with 2-loop or 3-loop hairy graphs. To detect these cycles, we use cocycles obtained by the 2-loop