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Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T14:09:22Z No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) / Made available in DSpace on 2018-05-02T14:09:22Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) Previous issue date: 2017-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / At the end of the 60s, Andr e and Quillen introduced a cohomology theory for commutative algebras, which today is called Andr e-Quillen's cohomology. In this work, we will study K ahler di erential functor, which is here seen as a derived functor (in a nonabelian context), which connects the categories: simpli ed R-algebras and simpli ed R-modules. In the rst, through simplicial resolutions, we will notice that they characterize certain objects and diagrams of this model category, which in turn, are preserved by K ahler di erential functor. In addition, we will approach the complex cotangent of a R-algebra, and through it, de ne the homology and cohomology of Andr e-Quilen, and of course, expose some properties of these. / No nal da década de 60, André e Quillen introduziram uma teoria de cohomologia para álgebras comutativas, que hoje recebe o nome de cohomologia de André-Quillen. Neste trabalho, estudaremos o funtor de diferenciais de K ahler, que aqui é visto como funtor derivado (em um contexto não abeliano), que conecta as categorias: R-álgebras simpliciais e R-m odulos simpliciais. Na primeira, atrav es das resolu c~oes simpliciais, notaremos que estas caracterizam certos objetos e diagramas desta categoria modelo, que por sua vez, s~ao preservados pelo funtor de diferenciais de K ahler. Al em disso, abordaremos o complexo cotangente de uma R- algebra, e atrav es dele, de nir a homologia e cohomologia de André-Quillen, e naturalmente, expor algumas propriedades destas.

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζp], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL2 → GL2 → GL1 → 1 we show that the calculation of the homology of SL2 gives information about this conjecture. We also present a series of algorithms that finds an upper bound on the second homology group of a finitely-presented group. In particular, given a finitely-presented group G, Hopf's formula expresses the second integral homology of G in terms of generators and relators; the algorithms exploit Hopf's formula to estimate H2(G; k), with coefficients in a finite field k. We conclude with sample calculations using the algorithms.

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United States Public Law 92-541, commonly known as the Teague-Cranston Act, called for the creation of five new medical schools in five states to meet the needs of medically under served areas of the country. The act, as passed, required that the new schools be "located in proximity to, and operated in conjunction with, Veterans' Administration medical facilities." This worked in ETSU's favor as the university is located adjacent to the Mountain Home VA Hospital. Signed into law by President Richard Nixon, this would eventually lead to the establishment of the Quillen College of Medicine.

Following the passage of the Teague-Cranston Act, on February 14, 1974 Senator Nave of the Tennessee General Assembly called for consideration of state legislation to establish a medical school at East Tennessee State University. Eventually passing both the Tennessee House and Senate, the bill was vetoed by Governor Winfield Dunn of Memphis. Motions to override the veto were made in both chambers and were successful. Senate Bill no.1549 became law on March 6, 1974.