Author | Cohen, Marshall M. author |
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Title | A Course in Simple-Homotopy Theory [electronic resource] / by Marshall M. Cohen |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1973 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9372-6 |
Descript | XI, 116 p. online resource |
I. Introduction -- ยง1. Homotopy equivalence -- ยง2. Whiteheadโs combinatorial approach to homotopy theory -- ยง3. CW complexes -- II. A Geometric Approach to Homotopy Theory -- ยง4. Formal deformations -- ยง5. Mapping cylinders and deformations -- ยง6. The Whitehead group of a CW comple -- ยง7. Simplifying a homotopically trivial CW pair -- ยง8. Matrices and formal deformations -- III. Algebra -- ยง9. Algebraic conventions -- ยง10. The groups KG(R) -- ยง11. Some information about Whitehead groups -- ยง12. Complexes with preferred bases [= (R,G)-complexes] -- ยง13. Acyclic chain complexes -- ยง14. Stable equivalence of acyclic chain complexes -- ยง15. Definition of the torsion of an acyclic comple -- ยง16. Milnorโs definition of torsion -- ยง17. Characterization of the torsion of a chain comple -- ยง18. Changing rings -- IV. Whitehead Torsion in the CW Category -- ยง19. The torsion of a CW pair โ definition -- ยง20. Fundamental properties of the torsion of a pair -- ยง21. The natural equivalence of Wh(L) and ? Wh (?1Lj) -- ยง22. The torsion of a homotopy equivalence -- ยง23. Product and sum theorems -- ยง24. The relationship between homotopy and simple-homotopy -- ยง25. Tnvariance of torsion, h-cobordisms and the Hauptvermutung -- V. Lens Spaces -- ยง26. Definition of lens spaces -- ยง27. The 3-dimensional spaces Lp,q -- ยง28. Cell structures and homology groups -- ยง29. Homotopy classification -- ยง30. Simple-homotopy equivalence of lens spaces -- ยง31. The complete classification -- Appendix: Chapmanโs proof of the topological invariance of Whitehead Torsion -- Selected Symbols and Abbreviations