Riemann, Topology, and Physics
This book combines a fascinating account of the work of Bernhard Riemann, one of history's foremost mathematicians, and a lucid discussion of the contemporary interaction of topology and physics. The first part of the book deals with the life and research activity of Riemann. The second part discusses applications of topology to contemporary physics.
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Abelian functions algebraic analytic function appeared arbitrary basic called cholesteric circle classical complex concept connected considered contemporary corresponding curvature curve deﬁned deﬁnition Dirichlet disk domain electrodynamics electromagnetic elementary particles Euler characteristic example existence ferromagnetism ﬁber bundles ﬁeld ﬁeld theory Figure ﬁgures ﬁnd ﬁnite ﬁrst gauge ﬁelds Gauss genus geometry given Gottingen Gottingen University gravitational hedgehog Higgs Higgs mechanism homeomorphic homotopy ideas inﬁnite inﬂuence integral interesting invariant investigation Klein liquid crystals magnetic manifolds massless mathematicians mathematics metric Mobius strip molecules monopole multivalued functions nematic neutron obtained order parameter phase transitions physicists physics Poincare point singularities problem projective plane properties proton quantum quarks reﬂection Riemann surface Riemannian rotations signiﬁcant simply-connected singular point solitons solution space space-time sphere spin spontaneous symmetry-breaking strong interactions structure sufﬁciently superconductivity superﬂuid symmetry group theorem tion topological methods torus transformations two-dimensional surface vacuum vector ﬁeld vortices wave Weierstrass