In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5  and proceeded to prove the h-cobordism theorem . This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes . Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
This book documents the United States Coast Guard career of Herbert E. Nolda, from his enlistment in April 1942 to his discharge in December 1945. The book also encompasses his early life before the war and his life after the war as it relates to veterans' matters. On the morning of December 7, 1941, Herbert was living in Santa Monica, California, where he was employed at the huge Douglas Aircraft factory. He arrived at a boarding house for lunch to find the landlady hysterical with the news of the bombing of Pearl Harbor. Several other young men were there too. Within minutes one of the young men stood up and announced: "Our country's in trouble and needs our help. I'm going down to enlist. Is anyone else coming with me?" "I am," Herbert replied. His time in the service was varied, from patrols on the East Coast, to four major invasions in North Africa and Europe. On June 6, 1944, D-Day, he was manning the #1 gun on his ship, LCI(L) #92 as she plowed into the maelstrom of Omaha Beach. Her sister ship, LCI(L) #91 had hit the beach a half hour earlier. She had been Herbert's home until a month before D-Day. The two small ships became famous in the annuals of D-Day. Later, in mid-August 1945, Herbert was aboard the troop transport, USS Admiral H.T. Mayo anchored at Ulithi Atoll in the South Pacific when the guns of the neighboring ships started firing, but there were no enemy planes in sight. . . This book is filled with the grim and the humorous incidents of war as experienced by a young sailor from landlocked Nebraska. Also interwoven are shorter biographies of some of Herbert's crewmembers. It is richly illustrated with 185 photographs and other historical documents.
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