Four-manifolds, Geometries and Knots
by Jonathan Hillman
Publisher: arXiv 2009
Number of pages: 396
The goal of this 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 manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery, geometries and geometric decompositions, and 2-knots.
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by Allen Hatcher
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.
by Nigel Hitchin
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.
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.
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.