**Topology:**

See Geometry & Topology Monographs for further study. Also consult Allen's list of recommended books on topology [.pdf].

In general:

- Hocking J.G. and Young G.S.
*Topology* - Kelley J.L.
*General Topology*- "What every young analyst should know" was the originally intended title. Morse-Kelley set theory was introduced in this book. - Steenrod N.
*The Topology of Fibre Bundles* - Stillwell J.
*Classical Topology and Combinatorial Group Theory*

Geometric Topology:

- Firby P.A. and Gardiner C.F.
*Surface Topology*- One quote by Ian Stewart is sufficient. "This book is in the top ten for books conveying the dreadful secret that mathematics is fascinating." - Gay D.
*Explorations in Topology: Map Coloring, Surfaces and Knots* - Ranicki A. History of Knot Theory (FREE!) - Contains dozens of historical material.
- Roberts J.D. Knots Knotes [.pdf] (FREE!)

Algebraic Topology:

- Bott R. and Tu L.W.
*Differential Forms in Algebraic Topology* - Dold A.
*Lectures on Algebraic Topology* - Eilenberg S. and Steenrod N.E.
*Foundations of Algebraic Topology* - Fulton W.
*Algebraic Topology: A First Course* - Hatcher A.
*Algebraic Topology*(here for FREE!) - Very beautiful book. - Lefschetz S.
*Algebraic Topology*(FREE!) - Lefschetz developed new result in this monograph. - Maunder C. R. F.
*Algebraic Topology* - Massey W.S.
*A Basic Course in Algebraic Topology* - Massey W.S.
*Algebraic Topology: An Introduction* - Mislin G. Algebraic Topology [.pdf] (FREE!)
- Moller J.M. Algebraic Topology Notes (FREE!)
- Munkres J.R.
*Elements of Algebraic Topology* - Spanier E.H.
*Algebraic Topology* - Switzer R.M.
*Algebraic Topology - Homology and Homotopy* - Vick J.W.
*Homology Theory: An Introduction to Algebraic Topology* - Wallace A.H.
*Algebraic Topology: Homology and Cohomology* - Wallace A.H.
*An Introduction to Algebraic Topology* - Whitehead G.H.
*Elements of Homotopy Theory* - Wilkins D.R. Algebraic Topology (FREE!)

K-theory:

- Hatcher A.
*Vector Bundles and K-theory*(FREE!) - Karoubi M.
*K-theory: An Introduction* - Rosenberg J.
*Algebraic K-Theory and Its Applications* - Srinivas V.
*Algebraic K-Theory* - Weibel C.
*The K-book: An Introduction to Algebraic K-theory*(FREE!)

Differential Topology:

- Brin M.G. Introduction to Differential Topology [.pdf] or [.ps] here (FREE!)
- Guillemin V. and Pollack A.
*Differential Topology* - Hirsch M.W.
*Differential Topology* - Kosinski A.A.
*Differential Manifolds*- An appendix by John W. Morgan on the work of Grigory Perelman is included in the 2007 Dover edition. - Lang S.
*Introduction to Differentiable Manifolds* - Milnor J.
*Morse Theory*- More advanced work, influential. Notes taken by M. Spivak and R. Wells. - Milnor J.W.
*Topology from the Differentiable Viewpoint*- As an introduction. - Wallace A.H.
*Differential Topology: First Steps* - 張筑生：《微分拓樸》

## 沒有留言:

張貼留言