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

By Martin Arkowitz

The unifying subject of this book is the Eckmann-Hilton duality concept, to not be came across because the motif of the other text.  given that many themes take place in twin pairs, this offers motivation for the information and decreases the volume of repetitious fabric. This rigorously written textual content strikes at a steady speed, despite relatively complicated fabric. moreover, 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 subject matters 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 publication 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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2. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2 H-Spaces and Co-H-Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. three Loop areas and Suspensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. four Homotopy teams I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. five Moore areas and Eilenberg–Mac Lane areas . . . . . . . . . . . . . 2. 6 Eckmann–Hilton Duality I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 35 36 forty four 50 60 sixty seven 70 three Cofibrations and Fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three. 2 Cofibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three. three Fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three. four Examples of Fiber Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three. five changing a Map via a Cofiber or Fiber Map . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seventy five seventy five seventy five eighty three ninety three 104 109 four targeted Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. 2 The Coexact and special series of a Map . . . . . . . . . . . . . . . . four. three activities and Coactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. four Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and fifteen one hundred fifteen 116 a hundred twenty five a hundred thirty xi xii Contents four. five Homotopy teams II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one hundred thirty five routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and fifty five functions of Exactness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five. 1 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five. 2 common Coefficient Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . five. three Homotopical Cohomology teams . . . . . . . . . . . . . . . . . . . . . . . . five. four purposes to Fiber and Cofiber Sequences . . . . . . . . . . . . . . . five. five The Operation of the basic crew . . . . . . . . . . . . . . . . . five. 6 Calculation of Homotopy teams . . . . . . . . . . . . . . . . . . . . . . . . . routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and fifty five a hundred and fifty five 156 one hundred 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 creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. 2 Homotopy Decompositions of areas . . . . . . . . . . . . . . . . . . . . . . 7. three Homology Decompositions of areas . . . . . . . . . . . . . . . . . . . . . . 7. four Homotopy and Homology Decompositions of Maps . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 workforce constitution in rX, Y s .

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