Noncommutative tachyons and K-theory

We show that the relation between D-branes and noncommutative tachyons lead s very naturally to the relation between D-branes and K-theory. We also dis cuss some relations between D-branes and K-homology, provide a noncommutati ve generalization of the ABS construction, and give a simple physical inter pretation of Bott periodicity. In addition, a framework for constructing Ne veu-Schwarz fivebranes as noncommutative solitons is proposed. (C) 2001 Ame rican Institute of Physics.