Book Manuscripts Available for Download:

Topics in Topology and Homotopy Theory:
This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology.

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Mathematical Aspects of General Relativity:
This book can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for self-study. The exposition is detailed and includes accounts of several topics of current interest, e.g., Lovelock theory and Ashtekar's variables.

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Bosonic Quantum Field Theory:
The purpose of this book is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role.

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Lagrangian Mechanics:
My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is differential geometric in character, the arena being the tangent bundle rather than the cotangent bundle. I have covered what I think are the basics. Points of detail are not swept under the rug but I have made an effort not to get bogged down in minutiae. Numerous examples have also been included.

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Positivity:
This book provides a systematic account of certain aspects of the statistical structure of quantum theory. Here the all prevailing notion is that of a completely positive map and Stinespring's famous characterization thereof. I have also included a systematic treatment of "quantum dynamical semigroups," culminating in Linblad's celebrated description of their generators.

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C*-Algebras:
This book is addressed to those readers who are already familiar with the elements of the theory but wish to go further. While some aspects, e.g. tensor products, are summarized without proof, others are dealt with in all detail. Numerous examples have been included and I have also appended an extensive list of references.

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Reconstruction Theory:
Suppose that G is a compact group. Denote by Rep G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operators--then Rep G is a monoidal *-category with certain properties P₁,P₂, ... . Conversely, if C is a monoidal *-category possessing properties P₁,P₂, ..., can one find a compact group G, unique up to isomorphism, such that Rep G "is" C? The central conclusion of reconstruction theory is that the answer is affirmative.

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Categorical Homotopy Theory:
This book is an account of certain developments in categorical homotopy theory that have taken place since the year 2000. Some aspects have been given the complete treatment (i.e., proofs in all detail), while others are merely surveyed. Therefore a lot of ground is covered in a relatively compact manner, thus giving the reader a feel for the "big picture" without getting bogged down in the "nitty-gritty."

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Homotopical Topos Theory:
The purpose of this book is two-fold: (1) To give a systematic introduction to topos theory from a purely categorical point of view, thus ignoring all logical and algebraic issues. (2) To give an account of the homotopy theory of the simplicial objects in a Grothendieck topos.

Download as PDF (4.69MB, 213 pages)

Fibrations and Sheaves:
The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials.

Download as PDF (4.20MB, 216 pages)