Computation of the Ruelle-Sullivan Map for Substitution Tilings

All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author. ii We study the dynamics of tiling spaces through cohomology. An adapta-tion of the Čech-deRham theorem allows us to compute the Ruelle-Sullivan map for such spaces and consider its image together with cohomology as a more useful invariant than cohomology alone. Computation of the map is performed for the Penrose tiling and the Octagonal tiling. Content