String rewriting systems and associated finiteness conditions

We begin with an introduction which describes the thesis in detail, and then a preliminary chapter in which we discuss rewriting systems, associated complexes and finiteness conditions. In particular, we recall the graph of derivations r and the 2- complex V associated to any rewriting system, and the related geometric finiteness conditions F DT and F HT. In §1.4 we give basic definitions and results about finite complete rewriting systems, that is, rewriting systems which rewrite any word in a finite number of steps to its normal form, the unique irreducible word in its congruence class. The main work of the thesis begins in Chapter 2 with some discussion of rewriting systems for groups which are confluent on the congruence class containing the empty word. In §2.1 we characterize groups admitting finite A-complete rewriting systems as those with a A-Dehn presentation, and in §2.2 we give some examples of finite rewriting systems for groups which are A-complete but not complete. For the remainder of the thesis, we study how the properties of finite complete rewriting systems which are discussed in the first chapter are mirrored in higher dimensions. In Chapter 3 we extend the 2-complex V to form a new 3-complex VP, and in Chapter 4 we define new finiteness conditions F DT2 and F HT2 based on the homotopy and homology of this complex. In §4.4 we show that if a monoid admits a finite complete rewriting system, then it is of type F DT2 • The final chapter contains a discussion of alternative ways to define such higher dimensional finiteness conditions. This leads to the introduction, in §5.2, of a variant of the Guba-Sapir homotopy reduction system which can be associated to any co~­ plete rewriting system. This is a rewriting system operating on paths in r, and is complete in the sense that it rewrites paths in a finite number of steps to a unique "normal form"

Creating Characters in a Story-Telling Universe

Extended story generation, i.e., the creation of continuing serials, presents difficult and interesting problems for Artificial Intelligence. We present here the first phase or the development of a program, UNIVERSE, that will ultimately tell extended stories. In particular, alter describing our overall model of story telling, we present a method for creating universes of characters appropriate for extended story generation. This method concentrates on the need to keep story-telling universes consistent and coherent. We also describe the information that must be maintained for characters and interpersonal relationships, and the use of stereotypical information about people to help motivate trait values. The use of historical events for motivation is also described. Finally, we present an example of a character generated by UNIVERSE

A computation of the action of the mapping class group on isotopy classes of curves and arcs in surfaces

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982.MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCEBibliography: leaves 155-156.by Robert Clack Penner.Ph.D

Subgroups defined by generating pairs of groups described by presentations

SIGLELD:D49529/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Shadows and quantum invariants

We investigate quantum invariants and their topolological applications through skein theory and the use of Turaev's shadows. We study knots and links in 3-manifold different from S^3, in particular we focus on the connected sum #_g(S^1xS^2) of g>=0 copies of S^1xS^2 and on the 3-torus T^3. Our main tools are the Kauffman bracket an the Turaev's shadows. An introductin and a surey to skein theory and Turaev's shadows is given. We present all the main open conjectures about topological applications of quantum invariants. Two theorems about links in S^3 are extended to links and colored knotted trivalent graphs in #_g(S^1xS^2). The first one is the Tait conjecture about crossing number and alternating links, and the second one is the Eisermann's theorem about ribon surfaces. Both are topological applications of the Jones polynomial. We compute the skein space of the 3-torus. Moreover we show the table of knots a links in S^1xSì2 with crossing number up to 3

K-State graduate catalog, 1997-1999

Course catalogs were published under the following titles: Catalogue of the officers and students of the Kansas State Agricultural College, with a brief history of the institution, 1st (1863/4); Annual catalogue of the officers and students of the Kansas State Agricultural College for, 2nd (1864/5)-4th (1868/9); Catalogue of the officers and students of the Kansas State Agricultural College for the year, 1869-1871/2; Hand-book of the Kansas State Agricultural College, Manhattan, Kansas, 1873/4; Biennial catalogue of the Kansas State Agricultural College, Manhattan, Kansas, calendar years, 1875/77; Catalogue of the State Agricultural College of Kansas, 1877/80-1896/97; Annual catalogue of the officers, students and graduates of the Kansas State Agricultural College, Manhattan, 35th (1897/98)-46th (1908/09); Catalogue, 47th (1909/10)-67th (1929/30); Complete catalogue number, 68th (1930/31)-81st (1943/1944); Catalogue, 1945/1946-1948/1949?; General catalogue, 1949/1950?-1958/1960; General catalog, 1960/1962-1990/1992. Course catalogs then split into undergraduate and graduate catalogs respectively: K-State undergraduate catalog, 1992/1994- ; K-State graduate catalog, 1993/1995-Citation: Kansas State University. (1997). K-State graduate catalog, 1997-1999. Manhattan, KS: Kansas State University.Call number: LD2668.A11711 K78