Total synthesis of the first molecular Moebius strip

On the Band Structure of Möbius Polymers

“…isomer have been formed [9], This result indicates some real chance for the formation of similar structures in the course of at least some polymerisations. In an earlier paper [10], we studied the electronic band structure of cylindrical polymers, termed "rota polymers" on that occasion.…”

“…Since the integrals corresponding to the o bonds between the first and the last monomeric units (expressed in AO's) do not change their sign in the R and the M form. (9) and (18) must be replaced by // = / , and in the last two lines of (14) the sign must be changed.…”

Toroidal embeddings of abstractly planar graphs are knotted or linked

“…[8][9][10][11][12][13][14][15][16][17][18][19]). Furthermore, crystal engineers have produced coordination networks that contain knots and links [6].…”

Symmetries of spatial graphs and Simon invariants

“…A study of symmetries of spatial graphs is not only a fundamental problem in low dimensional topology as a generalization of achirality of knots and links but also an important research theme from the standpoint of application to macromolecular chemistry, which is called molecular topology [23], [16], [1], [2]. Actually, both K 5 and K 3,3 have been realized chemically as underlying molecule graphs for some chemical compounds [14], [12], [24], [5]. We refer the reader to [15] for a pioneer work on symmetries of spatial embeddings of K 5 and K 3,3 .…”