{"product_id":"rational-homotopy-theory-and-differential-forms-revised-edition","title":"Rational Homotopy Theory and Differential Forms - Revised Edition","description":"\u003cp\u003eIn this review of Rational Homotopy Theory and Differential Forms, the reviewer finds a rigorous, modern exposition aimed at graduate students and researchers working in algebraic topology. The single biggest reason to buy this book is its careful connection between homotopy-theoretic ideas and differential forms, with the second edition providing updated appendices and a clarified proof of a Serre spectral sequence result. Readers looking for a focused, technical treatment of \u003cstrong\u003erational homotopy theory\u003c\/strong\u003e will appreciate the clarity and the inclusion of Sullivan's approach to computing rational homotopy type from forms.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eRevised appendices:\u003c\/strong\u003e The expanded discussion of the Hirsch lemma offers clearer background and makes several technical arguments more accessible for study and reference.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePostnikov and rational towers:\u003c\/strong\u003e Detailed treatment of Postnikov towers helps readers understand how rationalization interacts with classical homotopy decompositions.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDifferential forms focus:\u003c\/strong\u003e The book links differential forms to topology through de Rham theorems on simplicial complexes, strengthening computational intuition.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSullivan's results presented:\u003c\/strong\u003e A presentation of Sullivan's methods shows how to compute rational homotopy types directly from differential forms, useful for hands-on applications.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eCorrected and updated content:\u003c\/strong\u003e The second edition updates material throughout to reflect advances in homotopy theory, improving accuracy and topical relevance.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is best suited to graduate students in mathematics, and researchers in algebraic topology or differential geometry who already have some background in homotopy theory and differential forms. Its emphasis on modern approaches and updated appendices makes it a useful textbook for a reading course or a reference for active researchers.\u003c\/p\u003e\n\u003cp\u003eThose without prior exposure to basic algebraic topology or de Rham theory should look elsewhere for a more introductory treatment, since the text assumes familiarity with core topological and algebraic techniques rather than developing them from first principles.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eConcise presentation of \u003cstrong\u003ePostnikov towers\u003c\/strong\u003e and rationalization that clarifies conceptual structure.\u003c\/li\u003e\n\u003cli\u003eCareful link between differential forms and topology via de Rham-type results on simplicial complexes.\u003c\/li\u003e\n\u003cli\u003eUpdated appendices and corrected proofs increase reliability as a reference for researchers.\u003c\/li\u003e\n\u003cli\u003eIncludes Sullivan's computational methods, valuable for explicit computations in rational homotopy.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eDense, technical style assumes background knowledge and is not aimed at beginners.\u003c\/li\u003e\n\u003cli\u003eFocused scope means readers seeking broad introductions to algebraic topology may need supplemental texts.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eRational Homotopy Theory and Differential Forms\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003ePhillip Griffiths, John Morgan\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eEdition\u003c\/td\u003e\n\u003ctd\u003eSecond edition, revised and corrected\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eProgress in Mathematics, 16\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrimary topics\u003c\/td\u003e\n\u003ctd\u003eRational homotopy theory; differential forms; Postnikov towers\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eNew material\u003c\/td\u003e\n\u003ctd\u003eExpanded appendices, Hirsch lemma discussion, updated proofs\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eRational Homotopy Theory and Differential Forms is a strong, well-updated reference for graduate students and researchers who need a focused bridge between homotopy theory and differential forms. Its corrected proofs and expanded appendices make it good value for those seeking rigorous, usable presentations of Sullivan's methods and de Rham results on simplicial complexes.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this edition include new corrections?\u003c\/strong\u003e\u003cbr\u003eYes, the second edition is revised and corrected with expanded appendices and clarified proofs, including a fuller discussion of the Hirsch lemma.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs prior topology required?\u003c\/strong\u003e\u003cbr\u003eYes, readers should have background in basic algebraic topology and differential forms to follow the material comfortably.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes the book cover computational methods?\u003c\/strong\u003e\u003cbr\u003eIt presents Sullivan's approach to computing rational homotopy type from forms, making it useful for explicit computations.\u003c\/p\u003e","brand":"Phillip Griffiths, John Morgan","offers":[{"title":"Default Title","offer_id":48635653292251,"sku":"1493936999","price":139.77,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61gG6iM8lGL._SL1255.jpg?v=1778533704","url":"https:\/\/gearmusthave.com\/products\/rational-homotopy-theory-and-differential-forms-revised-edition","provider":"GearMustHave","version":"1.0","type":"link"}