On PL DeRham Theory and Rational Homotopy Type

On PL DeRham Theory and Rational Homotopy Type
Author :
Publisher : American Mathematical Soc.
Total Pages : 108
Release :
ISBN-10 : 9780821821794
ISBN-13 : 0821821792
Rating : 4/5 (94 Downloads)

Synopsis On PL DeRham Theory and Rational Homotopy Type by : Aldridge Knight Bousfield

The rational [bold]PL de Rham theory of Sullivan is developed and generalized, using methods of Quillen's "homotopical algebra." For a field k of characteristic 0, a pair of contravariant adjoint functors A : (Simplicial sets) [right arrow over left arrow] (Commutative DG k-algebras) : F is obtained which pass to the appropriate homotopy categories. When k is the field of rationals, these functors induce equivalence between the appropriate simplicial and algebraic rational homotopy categories. The theory is not restricted to simply connected spaces. It is closely related to the theory of "rational localization" (for nilpotent spaces) and "rational completion" in general.

Handbook of Algebraic Topology

Handbook of Algebraic Topology
Author :
Publisher : Elsevier
Total Pages : 1336
Release :
ISBN-10 : 9780080532981
ISBN-13 : 0080532985
Rating : 4/5 (81 Downloads)

Synopsis Handbook of Algebraic Topology by : I.M. James

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Algebraic Topology

Algebraic Topology
Author :
Publisher : Springer
Total Pages : 288
Release :
ISBN-10 : 9783540357377
ISBN-13 : 3540357378
Rating : 4/5 (77 Downloads)

Synopsis Algebraic Topology by : P. Hoffman

Singularities

Singularities
Author :
Publisher : American Mathematical Soc.
Total Pages : 378
Release :
ISBN-10 : 9780821850961
ISBN-13 : 0821850962
Rating : 4/5 (61 Downloads)

Synopsis Singularities by : University of Minnesota. Institute for Mathematics and Its Applications

Covers the proceedings of the Institute for Mathematics and its Applications Participating Institutions Conference on Singularities, held at the University of Iowa in July 1986. Suitable for researchers in various aspects of singularity theory, this work provides an overview of the state of singularity theory and details work in several subareas.

Rational Homotopy Theory and Differential Forms

Rational Homotopy Theory and Differential Forms
Author :
Publisher : Springer Science & Business Media
Total Pages : 228
Release :
ISBN-10 : 9781461484684
ISBN-13 : 1461484685
Rating : 4/5 (84 Downloads)

Synopsis Rational Homotopy Theory and Differential Forms by : Phillip Griffiths

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Notices of the American Mathematical Society

Notices of the American Mathematical Society
Author :
Publisher :
Total Pages : 764
Release :
ISBN-10 : UCAL:B3530687
ISBN-13 :
Rating : 4/5 (87 Downloads)

Synopsis Notices of the American Mathematical Society by : American Mathematical Society

Contains articles of significant interest to mathematicians, including reports on current mathematical research.