The Hauptvermutung is the conjecture that any triangulations of a poly hedron are combinatorially identical. The conjecture used to be formulated on the flip of the century, and till its solution used to be a significant challenge of topology. first and foremost, it was once tested for low-dimensional polyhedra, and it could were anticipated that furt her improvement of high-dimensional topology might bring about a verification in all dimensions. even though, in 1961 Milnor built high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung generally. those polyhedra weren't manifolds, leaving open the Hauptvermu tung for manifolds. the advance of surgical procedure thought ended in the disproof of the high-dimensional manifold Hauptvermutung within the past due 1960's. regrettably, the broadcast list of the manifold Hauptvermutung has been incomplete, as used to be forcefully mentioned by way of Novikov in his lecture on the Browder sixtieth birthday convention held at Princeton in March 1994. This quantity brings jointly the unique 1967 papers of Casson and Sulli van, and the 1968/1972 'Princeton notes at the Hauptvermutung' of Armstrong, Rourke and Cooke, making this paintings bodily available. those papers comprise a number of different effects that have develop into a part of the folklore yet of which proofs have by no means been released. my very own contribution is meant to function an intro duction to the Hauptvermutung, and in addition to offer an account of a few newer advancements within the zone. In getting ready the unique papers for book, in simple terms minimum adjustments of punctuation and so forth.
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