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Author : James Stasheff
Publisher : Springer
ISBN 13 : 3540363149
Total Pages : 100 pages
Book Rating : 4.5/5 (43 download)
Download or read book H-Spaces from a Homotopy Point of View written by James Stasheff and published by Springer. This book was released on 2006-11-15 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Francis Dudley Williams
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (89 download)
Download or read book Homotopy Commutativity of H-spaces written by Francis Dudley Williams and published by . This book was released on 1965 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Arkowitz
Publisher : Springer
ISBN 13 : 3540349685
Total Pages : 39 pages
Book Rating : 4.5/5 (43 download)
Download or read book Groups of Homotopy Classes written by M. Arkowitz and published by Springer. This book was released on 2006-12-08 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the sets that one encounters in homotopy classification problems have a natural group structure. Among these are the groups [A, nX] of homotopy classes of maps of a space A into a loop-space nx. Other examples are furnished by the groups (̃y) of homotopy classes of homotopy equivalences of a space Y with itself. The groups [A, nX] and (̃Y) are not necessarily abelian. It is our purpose to study these groups using a numerical invariant which can be defined for any group. This invariant, called the rank of a group, is a generalisation of the rank of a finitely generated abelian group. It tells whether or not the groups considered are finite and serves to distinguish two infinite groups. We express the rank of subgroups of [A, nX] and of C(Y) in terms of rational homology and homotopy invariants. The formulas which we obtain enable us to compute the rank in a large number of concrete cases. As the main application we establish several results on commutativity and homotopy-commutativity of H-spaces. Chapter 2 is purely algebraic. We recall the definition of the rank of a group and establish some of its properties. These facts, which may be found in the literature, are needed in later sections. Chapter 3 deals with the groups [A, nx] and the homomorphisms f*: [B, nl̃ ̃[A, nx] induced by maps f: A ̃B. We prove a general theorem on the rank of the intersection of coincidence subgroups (Theorem 3. 3).
Author : Francois Sigrist
Publisher : Springer
ISBN 13 : 3540366210
Total Pages : 165 pages
Book Rating : 4.5/5 (43 download)
Download or read book H - Spaces written by Francois Sigrist and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. M. James
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Ten Types of H-spaces written by I. M. James and published by . This book was released on 1959 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Slack
Publisher : American Mathematical Soc.
ISBN 13 : 0821825143
Total Pages : 125 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings written by Michael Slack and published by American Mathematical Soc.. This book was released on 1991 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a 2-connected homotopy commutative H-space with associative mod 2 homology ring and finitely generated mod 2 cohomology ring has acyclic mod 2 cohomology. This implies that a connected, homotopy commutative, homotopy associative H-space with finitely generated mod 2 cohomology ring is mod 2 homotopy equivalent to a product of Eilenberg-MacLane spaces, giving a complete classification of such spaces localized at the prime 2.
Author : Roy René Douglas
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (29 download)
Download or read book Homotopy-commutativity in H-spaces written by Roy René Douglas and published by . This book was released on 1965 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R.M. Kane
Publisher : North Holland
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.:/5 (44 download)
Download or read book The Homology of Hopf Spaces written by R.M. Kane and published by North Holland. This book was released on 1988-08 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces.
Author : Paul Selick
Publisher : American Mathematical Soc.
ISBN 13 : 9780821844366
Total Pages : 220 pages
Book Rating : 4.8/5 (443 download)
Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Author : Ioan James
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.3/5 (91 download)
Download or read book On Homotopy written by Ioan James and published by . This book was released on 1960 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Arkowitz
Publisher : Springer
ISBN 13 : 9783662159156
Total Pages : 44 pages
Book Rating : 4.1/5 (591 download)
Download or read book Groups of Homotopy Classes written by Martin Arkowitz and published by Springer. This book was released on 1964 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the sets that one encounters in homotopy classification problems have a natural group structure. Among these are the groups [A,nX] of homotopy classes of maps of a space A into a loop-space nx. Other examples are furnished by the groups ~(y) of homotopy classes of homotopy equivalences of a space Y with itself. The groups [A,nX] and ~(Y) are not necessarily abelian. It is our purpose to study these groups using a numerical invariant which can be defined for any group. This invariant, called the rank of a group, is a generalisation of the rank of a finitely generated abelian group. It tells whether or not the groups considered are finite and serves to distinguish two infinite groups. We express the rank of subgroups of [A,nX] and of C(Y) in terms of rational homology and homotopy invariants. The formulas which we obtain enable us to compute the rank in a large number of concrete cases. As the main application we establish several results on commutativity and homotopy-commutativity of H-spaces. Chapter 2 is purely algebraic. We recall the definition of the rank of a group and establish some of its properties. These facts, which may be found in the literature, are needed in later sections. Chapter 3 deals with the groups [A,nx] and the homomorphisms f*: [B,n~l ~ [A,nx] induced by maps f: A ~ B. We prove a general theorem on the rank of the intersection of coincidence subgroups (Theorem 3. 3).
Author : Peter Hilton
Publisher : Elsevier
ISBN 13 : 1483258742
Total Pages : 167 pages
Book Rating : 4.4/5 (832 download)
Download or read book Localization of Nilpotent Groups and Spaces written by Peter Hilton and published by Elsevier. This book was released on 2016-06-03 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.
Author :
Publisher : Elsevier
ISBN 13 : 008087133X
Total Pages : 235 pages
Book Rating : 4.0/5 (88 download)
Download or read book Hopf Spaces written by and published by Elsevier. This book was released on 1976-01-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf Spaces
Author : Jelena Grbikc
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (591 download)
Download or read book Universal Homotopy Associative, Homotopy Commutative H-spaces written by Jelena Grbikc and published by . This book was released on 2004 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph Neisendorfer
Publisher : American Mathematical Soc.
ISBN 13 : 0821822322
Total Pages : 73 pages
Book Rating : 4.8/5 (218 download)
Download or read book Primary Homotopy Theory written by Joseph Neisendorfer and published by American Mathematical Soc.. This book was released on 1980 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author gives a systematic exposition of homotopy groups with coefficients in a cyclic group [italic]Z or [italic]Z[subscript italic]k. The text pays particular attention to low-dimensional cases and trouble with the small primes. The book gives a complete treatment of some topics--such as Samelson products--with a view toward applications.
Author : Jie Wu
Publisher : American Mathematical Soc.
ISBN 13 : 0821832395
Total Pages : 148 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopy Theory of the Suspensions of the Projective Plane written by Jie Wu and published by American Mathematical Soc.. This book was released on 2003 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
Author : Victor Percy Snaith
Publisher : American Mathematical Soc.
ISBN 13 : 0821822802
Total Pages : 117 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic $K$-Theory and Localised Stable Homotopy Theory written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1983 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a homomorphism from the stable homotopy of the classifying space of the group of units in a ring to its algebraic [italic]K-theory. When the ring has enough roots of unity a "Bott element" exists in these groups (taken with coefficients). We compute the groups obtained by inverting the Bott element. This computation is used in conjunction with homomorphism to construct algebraic [italic]K-theory classes and to give upper bounds on [italic]K-theory with the Bott element inverted.
