The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accord- ingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to homotopy theory we also discuss by way of analogy cohomology with arbitrary coefficients. Although we have in mind an audience with prior exposure to algebraic or differential topology, for the most part a good knowledge of linear algebra, advanced calculus, and point-set topology should suffice. Some...
The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Acco...
From the Introduction: Marston Morse was born in 1892, so that he was 33 yearsold when in 1925 his paper Relations between the critical points of a real-valuedfunction of n independent variables appeared in the Transactions of theAmerican Mathematical Society. Thus Morse grew to maturity just at thetime when the subject of Analysis Situs was being shaped by such masters asPoincare, Veblen, L. E. J. Brouwer, G. D. Birkhoff, Lefschetz and Alexander, and it was Morse's genius and destiny to discover one of the most beautifuland far-reaching relations between this fledgling and...
From the Introduction: Marston Morse was born in 1892, so that he was 33 yearsold when in 1925 his paper Relations between the critical points o...
