106,594 research outputs found

    A remark on the connectedness of spheres in Cayley graphs

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    The aim of this small note is to prove an elementary yet useful properties of finitely presented groups. Let G be a finitely generated group with one end. Fix a (finite) generating set and let BnB_n be the ball of radius nn around ee. Let Bnc,∞B_n^{c,\infty} be the infinite connected component of the complement of BnB_n. Then G has connected spheres if there exists a r>0r >0 such that Bn+r∩Bnc,∞B_{n+r} \cap B_n^{c,\infty} is connected for all n≄0n \geq 0. This note shows that if G is finitely presented then it has connected spheres.Comment: 5p., 1 figur

    Memorializing Genocide I: Earlier Holocaust Documentaries

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    In this essay, I discuss in detail two of the earliest such documentaries: Death Mills (1945), directed by Billy Wilder; and Nazi Concentration Camps (1945), directed by George Stevens. Both film-makers were able to get direct footage of the newly-liberated concentration camps from the U.S. Army. Wilder served as a Colonel in the U.S. Army’s Psychological Warfare department in 1945 and was tasked with producing a documentary on the death camps as well as helping to restart Germany’s film industry. I next review the great French Holocaust documentary Night and Fog (1955), directed by Alain Resnais. This was a widely acclaimed film, winning the Prix Jean Vigo in 1956. Resnais employed a camp survivor (Jean Cayrol) to write the dialogue, and it is powerful, indeed, truly lyrical in places. The last film I review in the essay is a generally overlooked British Thames Television documentary, Genocide: 1941-1945 (1974), directed by Michael Darlow (and narrated by Sir Laurence Oliver). It was the first of the major Holocaust documentaries to focus on the point that the Nazi genocide targeted first and foremost the Jewish people, and to explore the development of Nazi racial theory, and the rise of the SS
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