The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gave a coherent treatment of the subject up to that time. About 1955 Milnor gave a construction of a universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal. During the five years from 1950 to 1955, Hirzebruch clarified the notion of characteristic class and used it to prove a general Riemann-Roch theorem for algebraic varieties. This was published in his Ergebnisse Monograph. A systematic development of characteristic classes and their applications to manifolds is given in Part III and is based on the approach of Hirze bruch as modified by Grothendieck.

Terror, heartbreak, deceit, rape, tragedy, despair and finding the will to survive. These are the driving forces in the lives of three very different women. Shelly is a talented young artist, attending school, and dreaming of a future career and a life with the man she is dating. Lynne, a mobility instructor at a school for blind children, is building a family with her husband and young son. Lora, a human resources professional, is living a magical life of travel, theatre, sailing, and great restaurants with the husband she loves. And then a new reality descends upon each of them. Will these three women take steps to move towards their tomorrows? Will Shelly find a way to rescue herself by changing the game from his to hers without his knowledge? Will Lynne provide the necessary care for a 3-pound baby on 7 different medications due to severely compromised lungs? Will Lora accept that her amazingly wonderful marriage has been a hoax and find a way to define a new existence for herself? Continued captivity, the breakdown of a family, and the choice to end a life could be the consequences of failure. Their stories cross time, entwine with other lives, and ultimately converge at a pivotal moment in each of their lives.

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.

The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.

"Turn precuts into patchwork with 12 fat quarter-friendly quilts"--cover.

It's the night before preschool, and a little boy named Billy is so nervous he can't fall asleep. The friends he makes the next day at school give him a reason not to sleep the next night, either: he's too excited about going back! The book's simple rhyming text and sweet illustrations will soothe any child's fears about the first day of school.