Download E-books The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (K-Monographs in Mathematics) PDF

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.

Show description

Read Online or Download The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (K-Monographs in Mathematics) PDF

Best Differential Geometry books

Surgery on Simply-Connected Manifolds

This e-book is an exposition of the means of surgical procedure on simply-connected tender manifolds. Systematic learn of differentiable manifolds utilizing those rules was once began through Milnor [45] and Wallace [68] and built commonly within the final ten years. it's now attainable to provide a pretty whole thought of simply-connected manifolds of size ~ five utilizing this strategy and that's what i'm going to try and start right here.

Lie Sphere Geometry: With Applications to Submanifolds (Universitext)

Thomas Cecil is a math professor with an unrivalled seize of Lie Sphere Geometry. right here, he presents a transparent and finished glossy remedy of the topic, in addition to its purposes to the learn of Euclidean submanifolds. It starts off with the development of the gap of spheres, together with the basic notions of orientated touch, parabolic pencils of spheres, and Lie sphere changes.

The Geometry of Kerr Black Holes (Dover Books on Physics)

This specified monograph by way of a famous UCLA professor examines intimately the math of Kerr black holes, which own the homes of mass and angular momentum yet hold no electric cost. appropriate for complex undergraduates and graduate scholars of arithmetic, physics, and astronomy in addition to specialist physicists, the self-contained remedy constitutes an creation to fashionable thoughts in differential geometry.

The Penrose Transform: Its Interaction with Representation Theory (Dover Books on Mathematics)

"Brings to the reader a big volume of data, good equipped and condensed into lower than 200 pages. " — Mathematical ReviewsIn contemporary a long time twistor thought has develop into an incredible concentration for college students of mathematical physics. valuable to twistor idea is the geometrical rework referred to as the Penrose remodel, named for its groundbreaking developer.

Additional resources for The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (K-Monographs in Mathematics)

Show sample text content

Rated 4.95 of 5 – based on 38 votes