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New Research on Three-Manifolds And Mathematics
New Research on Three-Manifolds And Mathematics
Date: 22 April 2011, 13:12

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Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics with an emphasis on three manifolds.
Mathematics has been behind many of humanity’s most significant advances in fields as
varied as genome sequencing, medical science, space exploration, and computer technology.
But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and
can we help shape that destiny? This book assembles carefully selected articles highlighting
and explaining cutting-edge research and scholarship in mathematics with an emphasis on
three manifolds.
Chapter 1 is an elaboration of the ideas and intuitions of Grothendieck and Weil
concerning the “arithmetic topology”. Given 3-dimensional manifold M fibering over the
circle the authors introduce an algebraic number field K =

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