Geometric Topology

e-books in Geometric Topology category

The Geometry and Topology of Braid Groups
by Jenny Wilson - University of Michigan , 2018
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.
(4807 views)

Knot Diagrammatics
by Louis H. Kauffman - arXiv , 2004
This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.
(7401 views)

Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov - arXiv , 2014
The purpose of this paper is to give an introduction to virtual knot theory and to record a collection of research problems that the authors have found fascinating. The paper introduces the theory and discusses some problems in that context.
(6790 views)

An Introduction to High Dimensional Knots
by Eiji Ogasa - arXiv , 2013
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.
(6904 views)

Knot Invariants and Higher Representation Theory
by Ben Webster - arXiv , 2013
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel...
(7618 views)

Surgical Methods in Rigidity
by F.T. Farrell - Springer , 1996
This book is an introduction to the topological rigidity theorem for compact non-positively curved Riemannian manifolds. It contains a quick informal account of the background material from surgery theory and controlled topology prerequesite.
(8182 views)

Lectures on Polyhedral Topology
by John R. Stallings - Tata Institute of Fundamental Research , 1967
These notes contain: The elementary theory of finite polyhedra in real vector spaces; A theory of 'general position' (approximation of maps), based on 'non-degeneracy'. A theory of 'regular neighbourhoods' in arbitrary polyhedra; etc.
(9623 views)

Ends of Complexes
by Bruce Hughes, Andrew Ranicki - Cambridge University Press , 2008
The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of mapping tori and telescopes.
(9811 views)

Geometric Topology: Localization, Periodicity and Galois Symmetry
by Dennis Sullivan - Springer , 2005
In 1970, Sullivan circulated this set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts. The notes remain worth reading for the fresh picture they provide for geometric topology.
(10322 views)

The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds
by A.A. Ranicki, et al, - Springer , 1996
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.
(9936 views)

Exotic Homology Manifolds
by Frank Quinn, Andrew Ranicki , 2006
Homology manifolds were developed in the 20th century to give a precise setting for Poincare's ideas on duality. They are investigated using algebraic and geometric methods. This volume is the proceedings of a workshop held in 2003.
(9536 views)

Lower K- and L-theory
by Andrew Ranicki - Cambridge University Press , 2001
This is the first treatment of the applications of the lower K- and L-groups to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. Only elementary constructions are used.
(10242 views)

Surgery on Compact Manifolds
by C.T.C. Wall, A. A. Ranicki - American Mathematical Society , 1999
This book represents an attempt to collect and systematize the methods and main applications of the method of surgery, insofar as compact (but not necessarily connected, simply connected or closed) manifolds are involved.
(9949 views)

Algebraic and Geometric Surgery
by Andrew Ranicki - Oxford University Press , 2002
Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.
(10652 views)

Algebraic L-theory and Topological Manifolds
by A. A. Ranicki - Cambridge University Press , 2011
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.
(10099 views)

Diffeomorphisms of Elliptic 3-Manifolds
by S. Hong, J. Kalliongis, D. McCullough, J. H. Rubinstein - arXiv , 2011
The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature. For any elliptic 3-manifold M, the inclusion from the isometry group of M to the diffeomorphism group of M is a homotopy equivalence.
(8916 views)

Notes on String Topology
by Ralph L. Cohen, Alexander A. Voronov - arXiv , 2005
This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research.
(10337 views)

Four-manifolds, Geometries and Knots
by Jonathan Hillman - arXiv , 2009
The goal of the book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such knots.
(12195 views)

A Primer on Mapping Class Groups
by Benson Farb, Dan Margalit - Princeton University Press , 2011
Our goal in this book is to explain as many important theorems, examples, and techniques as possible, as quickly and directly as possible, while at the same time giving (nearly) full details and keeping the text (nearly) selfcontained.
(11320 views)

Combinatorial Knot Theory
by Louis H. Kauffman - University of Illinois at Chicago , 2009
This book is an introduction to knot theory and to Witten's approach to knot theory via his functional integral. Contents: Topics in combinatorial knot theory; State Models and State Summations; Vassiliev Invariants and Witten's Functional Integral.
(11153 views)

Lectures on the Geometry of Manifolds
by Liviu I. Nicolaescu - World Scientific Publishing Company , 2009
An introduction to the most frequently used techniques in modern global geometry. Suited to the beginning graduate student, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.
(12849 views)

An Introduction to Algebraic Surgery
by Andrew Ranicki - arXiv , 2000
Browder-Novikov-Sullivan-Wall surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory.
(11171 views)

Foliations and the Geometry of 3-manifolds
by Danny Calegari - Oxford University Press , 2007
The book gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
(12531 views)

A Geometric Approach to Differential Forms
by David Bachman - arXiv , 2003
This is a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students.
(16312 views)

E 'Infinite' Ring Spaces and E 'Infinite' Ring Spectra
by J. P. May - Springer , 1977
The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.
(12411 views)

CDBooK: Introduction to Vassiliev Knot invariants
by S.Chmutov, S.Duzhin, J.Mostovoy - Ohio State Universit , 2009
An introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. Written for readers with no background in this area, and we care more about the basic notions than about more advanced material.
(11757 views)

Algebraic and Geometric Topology
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer , 1985
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
(16915 views)

Math That Makes You Go Wow
by M. Boittin, E. Callahan, D. Goldberg, J. Remes - Ohio State University , 1998
This is an innovative project by a group of Yale undergraduates: A Multi-Disciplinary Exploration of Non-Orientable Surfaces. The course is designed to be included as a short segment in a late middle school or early high school math course.
(15248 views)

High-dimensional Knot Theory
by Andrew Ranicki - Springer , 1998
This book is an introduction to high-dimensional knot theory. It uses surgery theory to provide a systematic exposition, and it serves as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
(13002 views)

Geometry of Surfaces
by Nigel Hitchin , 2013
Geometry of Surfaces by Nigel Hitchin is a textbook on surfaces. However the author is also going to try and consider surfaces intrinsically, or abstractly, and not necessarily embedded in three-dimensional Euclidean space.
(14754 views)

The Geometry and Topology of Three-Manifolds
by William P Thurston - Mathematical Sciences Research Institute , 2002
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.
(18616 views)

Notes on Basic 3-Manifold Topology
by Allen Hatcher , 2000
These pages are really just an early draft of the initial chapters of a real book on 3-manifolds. The text does contain a few things that aren't readily available elsewhere, like the Jaco-Shalen/Johannson torus decomposition theorem.
(10503 views)