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Solve the following problems and submit them in class by December 1, 2009:

Problem 1 With T, B^+ and R as below, write B^+ as a composition of T and two R's, using he basic TG operations d_e, u_e, and \#.


Problem 2 Show that the "topological boundary" operator \partial_T and the "crossing change" operator x_T of the class of November 5 are compositions of the basic TG operations d_e, u_e, and \# (you are also allowed to use "nullary" operations, otherwise known as "constants").

Problem 3 Write the third Reidemeister move R3 as a relation on Z(B_+).