Elliptic Curves

By:

Dale Husemoller

Format:

Paperback / softback

Series:

Graduate Texts in Mathematics,

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Description

There are three new appendices, one by Stefan Theisen on the role of Calabi– Yau manifolds in string theory and one by Otto Forster on the use of elliptic curves in computing theory and coding theory. In the third appendix we discuss the role of elliptic curves in homotopy theory. In these three introductions the reader can get a clue to the far-reaching implications of the theory of elliptic curves in mathematical sciences. During the ?nal production of this edition, the ICM 2002 manuscript of Mike Hopkins became available. This report outlines the role of elliptic curves in ho- topy theory. Elliptic curves appear in the form of the Weierstasse equation and its related changes of variable. The equations and the changes of variable are coded in an algebraic structure called a Hopf algebroid, and this Hopf algebroid is related to a cohomology theory called topological modular forms. Hopkins and his coworkers have used this theory in several directions, one being the explanation of elements in stable homotopy up to degree 60. In the third appendix we explain how what we described in Chapter 3 leads to the Weierstrass Hopf algebroid making a link with Hopkins’ paper.

Release date Australia

November 19th, 2010

Author

Dale Husemoller

Audience

Professional & Vocational

Edition

Softcover reprint of the original 2nd ed. 2004

Illustrations

XXII, 490 p.

Pages

490

Series

Graduate Texts in Mathematics,

Dimensions

156x234x26

ISBN-13

9781441930255

Product ID

9866936

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