This PDF book covers the
following topics related to Geometric Topology : Klee’s Trick, Manifold factors, Stable homeomorphisms and the annulus
conjecture, Cellular homology, Some elementary homotopy theory, Wall’s
finiteness obstruction, A weak Poincar´e Conjecture in high dimensions,
Stallings’ characterization of euclidean space, Whitehead torsion,
Siebenmann’s Thesis, Torus trickery 101 - local contractibility, Torus
trickery 102 – the Annulus Conjecture, Homotopy structures on manifolds,
etc.
This PDF book covers the
following topics related to Geometric Topology : Klee’s Trick, Manifold factors, Stable homeomorphisms and the annulus
conjecture, Cellular homology, Some elementary homotopy theory, Wall’s
finiteness obstruction, A weak Poincar´e Conjecture in high dimensions,
Stallings’ characterization of euclidean space, Whitehead torsion,
Siebenmann’s Thesis, Torus trickery 101 - local contractibility, Torus
trickery 102 – the Annulus Conjecture, Homotopy structures on manifolds,
etc.
This PDF book covers the following topics related to
Geometric Topology : Algebraic Constructions, Homotopy Theoretical
Localization, Completions in Homotopy Theory, Spherical Fibrations,
Algebraic Geometry, The Galois Group in Geometric Topology.
Author(s): Dennis Sullivan, Massachusetts
Institute of Technology
The aim of this book is to
introduce hyperbolic geometry and its applications to two- and three-manifolds
topology. Topics covered includes: Hyperbolic geometry, Hyperbolic space,
Hyperbolic manifolds, Thick-thin decomposition, The sphere at infinity,
Surfaces, Teichmuller space, Topology of three-manifolds, Seifert manifolds,
Constructions of three-manifolds, Three-manifolds, Mostow rigidity theorem,
Hyperbolic Dehn filling.
This note covers the following topics: Semifree finite group
actions on compact manifolds, Torsion in L-groups, Higher diagonal
approximations and skeletons of K(\pi,1)'s, Evaluating the Swan finiteness
obstruction for finite groups, A nonconnective delooping of algebraic
K-theory, The algebraic theory of torsion, Equivariant Moore spaces,
Triviality of the involution on SK_1 for periodic groups, Algebraic K-theory
of spaces Friedhelm Waldhausen, Oliver's formula and Minkowski's
theorem.
The book is
divided into two parts, called Algebra and Topology. In principle, it is
possible to start with the Introduction, and go on to the topology in Part II, referring back to Part I for novel algebraic concepts.
The intent of this lecture note is to describe the very strong
connection between geometry and lowdimensional topology in a way which will
be useful and accessible to graduate students and mathematicians working in
related fields, particularly 3-manifolds and Kleinian groups.