What's Next? (eBook)

The Mathematical Legacy of William P. Thurston

Dylan Thurston (Herausgeber)

eBook Download: PDF

2020
472 Seiten
Princeton University Press (Verlag)
978-0-691-18589-7 (ISBN)

Infos

William Thurston (1946-2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmuller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas.This book brings together papers delivered by his colleagues and former students at "e;What's Next? The Mathematical Legacy of Bill Thurston,"e; a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics-innovations that have had a profound and lasting impact on the mathematical community as a whole-and also features two papers based on Thurston's unfinished work in dynamics.

Produkt-Details

• Erscheint lt. Verlag: 7.7.2020
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Schlagworte: Arbitrarily large • asymptotic expansion • automorphism • Big O notation • braid group • Branch point • Central series • Characterization (mathematics) • character variety • cohomology • Cohomology operation • commutative property • conjecture • conjugacy class • convex hull • Covering space • Coxeter Group • Curvature • Dehn's lemma • Diagram (category theory) • Disjoint union • Eigenfunction • Endomorphism • Epimorphism • equivalence class • equivalence relation • Euclidean space • Extreme point • Faithful Representation • fiber bundle • free group • Free Product • fundamental group • Geometrization conjecture • Geometry • Haar measure • HNN extension • Homeomorphism • Homotopy • Hyperbolic 3-manifold • Hyperbolic Geometry • Hyperbolic manifold • hyperbolic space • Hypercube • I0 • Inclusion map • incompressible surface • Jordan Curve Theorem • JSJ decomposition • Julia set • Klein Bottle • Kleinian group • Lebesgue measure • Leech Lattice • Limit point • Lyapunov exponent • Mahler measure • Manifold decomposition • mapping cylinder • Marriage Theorem • Maxima and minima • Möbius strip • Möbius transformation • moduli space • Natural topology • Non-Euclidean geometry • Non-positive curvature • normal subgroup • Open set • Orientability • Pair of pants (mathematics) • perfect group • Pleated surface • polynomial • preorder • probability measure • Pullback (category theory) • Pullback (differential geometry) • Quadric • Quasiconvex function • quasi-isometry • rectangle • Riemannian manifold • Riemann surface • Saddle point • sectional curvature • Sign (mathematics) • simple algebra • Simply connected space • Special case • SUBGROUP • Subset • Symplectic Geometry • Theorem • Topology • Total order • Unit disk • Unit sphere • Upper and lower bounds • vector bundle
• ISBN-10: 0-691-18589-1 / 0691185891
• ISBN-13: 978-0-691-18589-7 / 9780691185897