The new student in differential and low-dimensional topology is
faced with a bewildering array of tools and loosely connected
theories. This short book presents the essential parts of each,
enabling the reader to become 'literate' in the field and begin
research as quickly as possible. The only prerequisite assumed is
an undergraduate algebraic topology course. The first half of the
text reviews basic notions of differential topology and culminates
with the classification of exotic seven-spheres. It then dives into
dimension three and knot theory. There then follows an introduction
to Heegaard Floer homology, a powerful collection of modern
invariants of three- and four-manifolds, and of knots, that has not
before appeared in an introductory textbook. The book concludes
with a glimpse of four-manifold theory. Students will find it an
exhilarating and authoritative guide to a broad swathe of the most
important topics in modern topology.
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