Papers on DeRham Theory
Author: Richard Martin Hain
Publisher:
Published: 1990
Total Pages: 328
ISBN-13:
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On PL DeRham Theory and Rational Homotopy Type
Author: Aldridge Knight Bousfield
Publisher: American Mathematical Soc.
Published: 1976
Total Pages: 108
ISBN-13: 0821821792
DOWNLOAD EBOOKThe 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.
Collected Papers of K.T. Chen
Author: Kuo-Tsai Chen
Publisher: Springer Science & Business Media
Published: 2001-06-21
Total Pages: 776
ISBN-13: 9780817640057
DOWNLOAD EBOOKKuo-Tsai Chen (1923-1987) is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. His work is intimately related to the theory of minimal models as developed by Dennis Sullivan, whose own work was in part inspired by the research of Chen. An outstanding and original mathematician, Chen's work falls naturally into three periods: his early work on group theory and links in the three sphere; his subsequent work on formal differential equations, which gradually developed into his most powerful and important work; and his work on iterated integrals and homotopy theory, which occupied him for the last twenty years of his life. The goal of Chen's iterated integrals program, which is a de Rham theory for path spaces, was to study the interaction of topology and analysis through path integration. The present volume is a comprehensive collection of Chen's mathematical publications preceded by an article, "The Life and Work of Kuo-Tsai Chen," placing his work and research interests into their proper context and demonstrating the power and scope of his influence.
The Theory of Finslerian Laplacians and Applications
Author: P.L. Antonelli
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 305
ISBN-13: 9401152829
DOWNLOAD EBOOKFinslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
Raoul Bott: Collected Papers
Author: Loring W. Tu
Publisher: Birkhäuser
Published: 2018-03-26
Total Pages: 664
ISBN-13: 3319517813
DOWNLOAD EBOOKThis book is the fifth and final volume of Raoul Bott’s Collected Papers. It collects all of Bott’s published articles since 1991 as well as some articles published earlier but missing in the earlier volumes. The volume also contains interviews with Raoul Bott, several of his previously unpublished speeches, commentaries by his collaborators such as Alberto Cattaneo and Jonathan Weitsman on their joint articles with Bott, Michael Atiyah’s obituary of Raoul Bott, Loring Tu’s authorized biography of Raoul Bott, and reminiscences of Raoul Bott by his friends, students, colleagues, and collaborators, among them Stephen Smale, David Mumford, Arthur Jaffe, Shing-Tung Yau, and Loring Tu. The mathematical articles, many inspired by physics, encompass stable vector bundles, knot and manifold invariants, equivariant cohomology, and loop spaces. The nonmathematical contributions give a sense of Bott’s approach to mathematics, style, personality, zest for life, and humanity. In one of the articles, from the vantage point of his later years, Raoul Bott gives a tour-de-force historical account of one of his greatest achievements, the Bott periodicity theorem. A large number of the articles originally appeared in hard-to-find conference proceedings or journals. This volume makes them all easily accessible. It also features a collection of photographs giving a panoramic view of Raoul Bott's life and his interaction with other mathematicians.
Mathematics Related to Physics
Author: Raoul Bott
Publisher: Springer Science & Business Media
Published: 1994-12-19
Total Pages: 524
ISBN-13: 9780817636487
DOWNLOAD EBOOKThe Collected Papers of Raoul Bott are contained in five volumes, with each volume covering a different subject and each representing approximately a decade of Bott's work. The volumes are: Volume 1: Topology and Lie Groups (1950's) Volume 2: Differential Operators (1960's) Volume 3: Foliations (1970's) Volume 4: Mathematics Related to Physics (1980's) Volume 5: Completive Articles and Additional Biographic Material (1990's) Most of the papers in this volume deal with two physical-inspired themes: the Yang-Mills equations and the rigidity phenomena of vector bundles. It also contains Bott's own commentaries on a few of the papers, as well as a tribute by Clifford Taubes.
From Calculus to Cohomology
Author: Ib H. Madsen
Publisher: Cambridge University Press
Published: 1997-03-13
Total Pages: 302
ISBN-13: 9780521589567
DOWNLOAD EBOOKAn introductory textbook on cohomology and curvature with emphasis on applications.
Lie Groups, Geometry, and Representation Theory
Author: Victor G. Kac
Publisher: Springer
Published: 2018-12-12
Total Pages: 545
ISBN-13: 3030021912
DOWNLOAD EBOOKThis volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
Theories of Population from Raleigh to Arthur Young
Author: James Bonar
Publisher: Routledge
Published: 2014-01-14
Total Pages: 132
ISBN-13: 1136925244
DOWNLOAD EBOOKFirst Published in 1966. A book which deals with the thought and theories of leading men 17th and 18th century England, on the subjects of population and vital statistics. Beginning with Raleigh, Bacon and Hobbes, it passes to Harrington, Graunt and Halley. Then after Derham and Sussmilch, it treats the disputes of Hume and Wallace, Price and Arthur Young over Ancient and Modern Populousness.
Reading the Skies
Author: Vladimir Jankovic
Publisher: University of Chicago Press
Published: 2001-04-19
Total Pages: 296
ISBN-13: 9780226392158
DOWNLOAD EBOOKFrom the time of Aristotle until the late eighteenth century, meteorology meant the study of "meteors"—spectacular objects in the skies beneath the moon, which included everything from shooting stars to hailstorms. In Reading the Skies, Vladimir Jankovic traces the history of this meteorological tradition in Enlightenment Britain, examining its scientific and cultural significance. Jankovic interweaves classical traditions, folk/popular beliefs and practices, and the increasingly quantitative approaches of urban university men to understanding the wonders of the skies. He places special emphasis on the role that detailed meteorological observations played in natural history and chorography, or local geography; in religious and political debates; and in agriculture. Drawing on a number of archival sources, including correspondence and weather diaries, as well as contemporary pamphlets, tracts, and other printed sources reporting prodigious phenomena in the skies, this book will interest historians of science, Britain, and the environment.
