**National Medal of Science - Mathematics and Computer Science 1987**

American mathematician. Proof of Poincare Conjecture in dimension four. One of the greatest achievements in mathematics in this century. Fields Medal, 1986.

Books

Title:

Topoology of 4-Manifolds (PMS-39)

Volume 39 of Princeton Legacy Library

Volume 39 of Princeton Mathematical

Volume 39 of Princeton Legacy Library

Volume 39 of Princeton Mathematical

Authors:

Michael H. Freedman, Frank Quinn

Publisher:

Princeton University Press, 2014

ISBN:

1400861063, 9781400861064

Length:

272 pages

Subjects

Mathematics Topology

Summary : One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field.

Originally published in 1990.

Summary : One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field.

Originally published in 1990.

Title:

Selected Applications of Geometry to Low-dimensional Topology

Marker Lectures in the Mathematical Sciences. The Pennsylvania State University

University lecture series, ISSN 1047-3998

Marker Lectures in the Mathematical Sciences. The Pennsylvania State University

University lecture series, ISSN 1047-3998

Authors:

Michael H. Freednam, Feng Luo

Edition

Reprint

Publisher:

American Mathematica Soc., 1989

ISBN:

0821870009, 9780821870006

Length:

79 pages

Subjects

Mathematics General

Summary: This book, the inaugural volume in the University Lecture Series, is based on lectures presented at Pennsylvania State University in February 1987. The lectures attempt to give a taste of the accomplishments of manifold topology over the last 30 years. By the late 1950s, algebra and topology had produced a successful and beautiful fusion. Geometric methods and insight, now vitally important in topology, encompass analytic objects such as instantons and minimal surfaces, as well as nondifferentiable constructions. Keeping technical details to a minimum, the authors lead the reader on a fascinating exploration of several developments in geometric topology. They begin with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceed to the topology and geometry of foliated 3-manifolds. They also explain, in terms of general position, why four-dimensional space has special attributes, and they examine the insight Donaldson theory brings. The book ends with a chapter on exotic structures on $\mathbf R^4$, with a discussion of the two competing theories of four-dimensional manifolds, one topological and one smooth. Background material was added to clarify the discussions in the lectures, and references for more detailed study are included. Suitable for graduate students and researchers in mathematics and the physical sciences, the book requires only background in undergraduate mathematics. It should prove valuable for those wishing a not-too-technical introduction to this vital area of current research.

Summary: This book, the inaugural volume in the University Lecture Series, is based on lectures presented at Pennsylvania State University in February 1987. The lectures attempt to give a taste of the accomplishments of manifold topology over the last 30 years. By the late 1950s, algebra and topology had produced a successful and beautiful fusion. Geometric methods and insight, now vitally important in topology, encompass analytic objects such as instantons and minimal surfaces, as well as nondifferentiable constructions. Keeping technical details to a minimum, the authors lead the reader on a fascinating exploration of several developments in geometric topology. They begin with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceed to the topology and geometry of foliated 3-manifolds. They also explain, in terms of general position, why four-dimensional space has special attributes, and they examine the insight Donaldson theory brings. The book ends with a chapter on exotic structures on $\mathbf R^4$, with a discussion of the two competing theories of four-dimensional manifolds, one topological and one smooth. Background material was added to clarify the discussions in the lectures, and references for more detailed study are included. Suitable for graduate students and researchers in mathematics and the physical sciences, the book requires only background in undergraduate mathematics. It should prove valuable for those wishing a not-too-technical introduction to this vital area of current research.

Michael H. Freedman

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Photo: Courtesy Michael H. Freedman

**Name:** Michael Hartley Freednam

**Birth:** 21 April 1951 Los Angeles, CA USA

**Institution when prize awarded:** University of California, San Diego

**Citation:** "For his proof of the Poincare Conjecture in dimension four: a topological four-manifold is homeomorphic to S4 [4th power]. It is homotopy equivalent to S4 [4th power], one of the greatest achievements in mathematics in this century." Presented by President Reagan at a White House Ceremony on June 25, 1987.

**Field**: Mathematics and Computer Science

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