Download E-books Introduction to Homotopy Theory (Universitext) PDF

By Martin Arkowitz

The unifying topic of this book is the Eckmann-Hilton duality thought, to not be stumbled on because the motif of the other text.  due to the fact that many themes take place in twin pairs, this gives motivation for the guidelines and decreases the quantity of repetitious fabric. This rigorously written textual content strikes at a steady speed, inspite of quite complicated fabric. additionally, there's a wealth of illustrations and workouts. The more challenging workouts are starred, and tricks to them are given on the finish of the book.
Key issues include:
*basic homotopy
*H-Spaces and Co-H-Spaces;
*cofibrations and fibrations;
*exact sequences;
*applications of exactness;
*homotopy pushouts and pullbacks and
 the classical theorems of homotopy theory;
*homotopy and homology decompositions;
*homotopy units; and
*obstruction theory.
The e-book is written as a textual content for a moment direction in algebraic topology, for a subject matters seminar in homotopy concept, or for self guideline.

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Four. 1 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. 2 The Coexact and certain series of a Map . . . . . . . . . . . . . . . . four. three activities and Coactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. four Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and fifteen a hundred and fifteen 116 one hundred twenty five a hundred thirty xi xii Contents four. five Homotopy teams II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred thirty five routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one hundred fifty five functions of Exactness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five. 1 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five. 2 common Coefficient Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . five. three Homotopical Cohomology teams . . . . . . . . . . . . . . . . . . . . . . . . five. four purposes to Fiber and Cofiber Sequences . . . . . . . . . . . . . . . five. five The Operation of the elemental team . . . . . . . . . . . . . . . . . five. 6 Calculation of Homotopy teams . . . . . . . . . . . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and fifty five a hundred and fifty five 156 a hundred and sixty 163 169 177 a hundred ninety 6 Homotopy Pushouts and Pullbacks . . . . . . . . . . . . . . . . . . . . . . . 6. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Homotopy Pushouts and Pullbacks I . . . . . . . . . . . . . . . . . . . . . . 6. three Homotopy Pushouts and Pullbacks II . . . . . . . . . . . . . . . . . . . . . 6. four Theorems of Serre, Hurewicz, and Blakers–Massey . . . . . . . . . 6. five Eckmann–Hilton Duality II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 195 196 207 214 225 227 7 Homotopy and Homology Decompositions . . . . . . . . . . . . . . . . 7. 1 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. 2 Homotopy Decompositions of areas . . . . . . . . . . . . . . . . . . . . . . 7. three Homology Decompositions of areas . . . . . . . . . . . . . . . . . . . . . . 7. four Homotopy and Homology Decompositions of Maps . . . . . . . . . . routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 233 234 247 254 264 eight Homotopy units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. 2 The Set rX, Y s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. three type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four Loop and crew constitution in rX, Y s . . . . . . . . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 267 267 270 275 279 nine Obstruction thought . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. 1 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. 2 Obstructions utilizing Homotopy Decompositions . . . . . . . . . . . . . nine. three Lifts and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. four Obstruction Miscellany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 283 284 288 291 296 A Point-Set Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 B the basic staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 C Homology and Cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Contents xiii D Homotopy teams of the n-Sphere . . . . . . . . . . . . . . . . . . . . . . . . 312 E Homotopy Pushouts and Pullbacks . . . . . . . . . . . . . . . . . . . . . . . 314 F different types and Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 tricks to a couple of the routines . . . . . . . . . . . .

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