Low Dimensional Topology (Google eBook)

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Tomasz Mrowka, Peter Steven Ozsváth
American Mathematical Soc., Jan 1, 2009 - Mathematics - 315 pages
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Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.
  

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Contents

II
1
III
7
IV
21
V
25
VI
31
VII
37
VIII
43
IX
51
XIX
139
XX
143
XXI
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XXII
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XXIII
169
XXIV
177
XXV
185
XXVI
197

X
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XI
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XII
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XIII
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XIV
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XV
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XVI
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XVII
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XVIII
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XXVII
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XXVIII
265
XXIX
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XXX
275
XXXI
283
XXXII
291
XXXIII
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XXXIV
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About the author (2009)

Tomasz Mrowka is Professor of Mathematics at Massachusetts Institute of Technology. He holds the James and Marilyn Simons Professorship of Mathematics and is a Member of the American Academy of Arts and Sciences. He was a joint recipient (with Peter Kronheimer) of the 2007 Oswald Veblen Prize. His research interests are low-dimensional topology, partial differential equations and mathematical physics.

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