The Adams Spectral Sequence for Topological Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Adams Spectral Sequence for Topological Modular Forms write by Robert R. Bruner. This book was released on 2021-12-23. The Adams Spectral Sequence for Topological Modular Forms available in PDF, EPUB and Kindle. The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.
The Adams Spectral Sequence for Topological Modular Forms
The Adams Spectral Sequence for Topological Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Adams Spectral Sequence for Topological Modular Forms write by Robert Ray Bruner. This book was released on 2021. The Adams Spectral Sequence for Topological Modular Forms available in PDF, EPUB and Kindle.
Topological Modular Forms
Topological Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Modular Forms write by Christopher L. Douglas. This book was released on 2014-12-04. Topological Modular Forms available in PDF, EPUB and Kindle. The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Adams Memorial Symposium on Algebraic Topology
Adams Memorial Symposium on Algebraic Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adams Memorial Symposium on Algebraic Topology write by Nigel Ray. This book was released on 1992. Adams Memorial Symposium on Algebraic Topology available in PDF, EPUB and Kindle. J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the symposium; the articles contained here range from overviews to reports of work still in progress, as well as a survey and complete bibliography of Adams' own work. These proceedings form an important compendium of current research in algebraic topology, and.
A User's Guide to Spectral Sequences
A User's Guide to Spectral Sequences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A User's Guide to Spectral Sequences write by John McCleary. This book was released on 2001. A User's Guide to Spectral Sequences available in PDF, EPUB and Kindle. Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
