Rational Homotopical Models and Uniqueness
Rational Homotopical Models and Uniqueness

Author: Martin Majewski

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 175

ISBN-13: 0821819208

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The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.

Lectures on Algebraic Topology
Lectures on Algebraic Topology

Author: Albrecht Dold

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 390

ISBN-13: 3642678211

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Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.

Acyclic Models
Acyclic Models

Author: Michael Barr

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 194

ISBN-13: 0821828770

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Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology. The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.

Introduction to Structural Equation Modeling Using IBM SPSS Statistics and Amos
Introduction to Structural Equation Modeling Using IBM SPSS Statistics and Amos

Author: Niels Blunch

Publisher: SAGE

Published: 2012-11-09

Total Pages: 314

ISBN-13: 1446271846

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This comprehensive Second Edition offers readers a complete guide to carrying out research projects involving structural equation modeling (SEM). Updated to include extensive analysis of AMOS′ graphical interface, a new chapter on latent curve models and detailed explanations of the structural equation modeling process, this second edition is the ideal guide for those new to the field. The book includes: Learning objectives, key concepts and questions for further discussion in each chapter. Helpful diagrams and screenshots to expand on concepts covered in the texts. Real life examples from a variety of disciplines to show how SEM is applied in real research contexts. Exercises for each chapter on an accompanying companion website. A new glossary. Assuming no previous experience of the subject, and a minimum of mathematical knowledge, this is the ideal guide for those new to SEM and an invaluable companion for students taking introductory SEM courses in any discipline. Niels J. Blunch was formerly in the Department of Marketing and Statistics at the University of Aarhus, Denmark

Elements of Homology Theory
Elements of Homology Theory

Author: Viktor Vasilʹevich Prasolov

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 432

ISBN-13: 0821838121

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The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Introduction to Homotopy Theory
Introduction to Homotopy Theory

Author: Paul Selick

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 220

ISBN-13: 9780821844366

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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.

Homology Theory
Homology Theory

Author: P. J. Hilton

Publisher: CUP Archive

Published: 1967

Total Pages: 504

ISBN-13: 9780521094221

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This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

Introduction to Structural Equation Modeling Using IBM SPSS Statistics and EQS
Introduction to Structural Equation Modeling Using IBM SPSS Statistics and EQS

Author: Niels J. Blunch

Publisher: SAGE

Published: 2015-10-15

Total Pages: 361

ISBN-13: 1473943302

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This student orientated guide to structural equation modeling promotes theoretical understanding and inspires students with the confidence to successfully apply SEM. Assuming no previous experience, and a minimum of mathematical knowledge, this is an invaluable companion for students taking introductory SEM courses in any discipline. Niels Blunch shines a light on each step of the structural equation modeling process, providing a detailed introduction to SPSS and EQS with a focus on EQS′ excellent graphical interface. He also sets out best practice for data entry and programming, and uses real life data to show how SEM is applied in research. The book includes: Learning objectives, key concepts and questions for further discussion in each chapter. Helpful diagrams and screenshots to expand on concepts covered in the texts. A wide variety of examples from multiple disciplines and real world contexts. Exercises for each chapter on an accompanying . A detailed glossary. Clear, engaging and built around key software, this is an ideal introduction for anyone new to SEM.