Product Description
Consists of translations of several of Dehn's important papers on algebraic topology and group theory, and of excerpts from some lecture notes written by Dehn on group theory and the topology of surfaces. The papers cover Dehn's research on discontinuous groups, transformation of curves, knot theory, and the group of mapping classes. ... Read more

Customer Reviews (1)

Some delightful topology from the good old days
Dehn's work is centred around the deep and beautiful harmony between topology and combinatorial group theory. The connection manifests itself in the study of curves on surfaces. Here two central group theoretical problems crystallises: the word problem (corresponding to the topological problem of deciding whether a curve contracts to a point) and the conjugacy problem (topologically, to decide whether two given curves are conjugate). Dehn illuminates the situation with the wonderful idea of the group diagram. The investigations are given an even more geometrical feel through the use of hyperbolic geometry, which is prompted from within both group theory (the natural domain in which to draw many group diagrams) and topology (universal covering surface). We get to meet all these things in the form of lectures delivered before the publications. But these ideas have much greater scope and power, as Dehn shows in his impressive paper "On the Topology of three-dimensional Space" (1910). Here, of course, knots become important. This will soon (1912) lead Dehn to add a third item to his list of the fundamental problems of combinatorial group theory: the isomorphism problem. But wait a minute, you say, even a solution to this problem would not suffice to tell all knots apart. Well, Dehn is way ahead of you: in his 1914 paper he shows that the trefoil knot cannot be deformed into its mirror image. The two last papers are on mapping class groups of surfaces. Perhaps Dehn wanted to repeat his early success by returning to surface topology---the fountain of youth---to again come up with a clever combinatorialisation, this time of the mapping class group. I for one was less impressed the second time around.

There are introductions to each paper by Stillwell. These are very helpful, but short and intended primarily for experts. Fortunately for us non-experts who just want to read some beautiful mathematics, Stillwell's book "Classical Topology and Combinatorial Group Theory" is an excellent guide. ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Kathryn Grayson, Eugene E. Campbell, Ed Dorn, Dan Morse, Max Dehn, N. Randy Smith, Richard D. Hansen, Michael Waterman, J. Donald R. de Raadt, Corey Schou, Jeffrey Meldrum, Richard Holmer, Alan Steinberg, Brian Attebery. Excerpt:Dr. Alan Steinberg is an American author. He has published Divided , a collection of short stories, and Cry of the Leopard, a novel. In addition an opera of The Falcon and the Sailor Boy, for which Steinberg wrote the libretto , was recently performed at SUNY Potsdam , starring Stephanie Blythe . Steinberg received his PhD from Carnegie Mellon University, and is a Professor in SUNY Potsdam 's English department, where he also serves as the coordinator of the writing program. Steinberg has previously taught at Paul Smith's College, Marist College, and Idaho State University . He is a virgin Works Alan Steinberg has published the following works of fiction: Steinberg has published numerous other short works and essays in various journals. A hyperlinked version of this chapter is at Brian Attebery is an academic writer on science fiction and fantasy fiction . He is professor of English at Idaho State University . His 1979 doctorate from Brown University was in American Civilization. Works Websites (URLs online) A hyperlinked version of this chapter is at Corey Schou is University Professor of Informatics and Associate Dean at Idaho State University , director of the National Information Assurance Training and Education Center (NIATEC) and the Simplot Decision Support Center (SDSC), and chair of the Colloquium for Information Systems Security Education (CISSE). Professor Schou's work is recognized as foundational to the Information Assurance discipline in academia. His work for three decades has resulted in standards used internationally by government, ind... ... Read more

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15-page booklet illustrated with black-and-white reproductions of prints. Features work by: Joan Sloan, Andre Ruellan, A. W. Heintzelman, Eugene Berman, Howard Cook, Max Kahn, Adolf Dehn, Martin Jackson, Yasuo Kuniyoshi, Benton Spruance, Misch Kohn, Federico Castellon, Franklin C. Watkins, Harold Paris, Wanda Gag, Milton Goldstein, Morris Blackburn, Fred Becker, and Josef Albers. ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: William Gropper, Max Kahn, Nathaniel Currier, John Henry Bufford, Adolf Dehn, Napoleon Sarony, William Sommer, Ettore Degrazia, Stow Wengenroth, Joseph Dixon, James Merritt Ives, Joseph Pennell, Benjamin Russell, John Bachmann, Louis Maurer, L. B. Cole, Richard Sedlon, Otto Stark, Charles Kassler, Wedo Georgetti, John Caspar Wild, Bernarda Bryson Shahn, Walter Ufer. Excerpt:Adolf Dehn, Landscape with Farm, 1947, watercolor, photo by Prof. Joseph Bonfanti. Adolf Dehn was born in Minnesota, November 22, 1895 and he died in New York City, May 19 1968. He was one of the most notable lithographers of the 20th century. Throughout his artistic career, Dehn participated in and helped define some important movements in American art, including Regionalism , Social Realism , and caricature . He was known for both his technical skills and his high-spirited, droll depictions of human foibles. Biography Dehn was born in 1895 in Waterville, Minnesota . Dehn began creating artwork at the age of six and by the time of his death had created nearly 650 images. After high school he went to the Minneapolis School of Art , known today as the (Minneapolis College of Art and Design) where he met Wanda Gág . Later he and Gag were two of only a dozen students in the country to earn a scholarship to the Art Students League of New York . After graduation, he was drafted to serve in World War I , but he was a conscientious objector . Dehn was imprisoned for two years for refusing to serve in the military. Early career After the war was over, he went to Europe. In Paris and Vienna he belonged to a group of intellectuals and artists, including E.E. Cummings . A number of the caricatures he drew depicting the Roaring 20s , burlesque, opera houses, and the café scene appeared in such magazines as Vanity Fair.... ... Read more