The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds
by A.A. Ranicki, et al,
Publisher: Springer 1996
Number of pages: 194
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions.
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by William P Thurston - Mathematical Sciences Research Institute
The text describes the connection between geometry and lowdimensional topology, it is useful to graduate students and mathematicians working in related fields, particularly 3-manifolds and Kleinian groups. Much of the material or technique is new.
by A. A. Ranicki - Cambridge University Press
Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds.
by Jenny Wilson - University of Michigan
Contents: Five definitions of the braid group; The topology of Fn(C); The integral cohomology of the pure braid group; Generalizations of PBn and their cohomology; Transfer and twisted coefficients; Stability in the cohomology of braid groups; etc.
by Eiji Ogasa - arXiv
This is an introductory article on high dimensional knots for the beginners. Is there a nontrivial high dimensional knot? We first answer this question. We explain local moves on high dimensional knots and the projections of high dimensional knots.