Algebraic Topology from a Homotopical Viewpoint

16This is an introductory text for a first course in algebraic topology. The authors present the beginning material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This point of view clearly has applications in algebraic geometry as understood by Lawson and Voevodsky. This carefully written book can be read by any student who knows some topology. It will be a useful place to quickly learn this novel homotopy-theoretic point of view of algebraic topology.04From the contents:Introduction.- Basic Concepts and Notation.- Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy Groups.- Homotopy Extension and Lifting Properties.- CW-Complexes Homology.- Homotopy Properties of CW-Complexes.- Cohomology Groups and Related Topics.- Vector Bundles.- K-Theory.- Adams Operations and Applications.- Relations Between Cohomology and Vector Bundles.- Cohomology Theories and Brown Representability.- Appendix A: Proof of the Dold-Thom Theorem.- Appendix B: Proof of the Bott Periodicity Theorem.- References.- Index.- Glossary.