nLab

Background Basic concepts Universal constructions Local presentation Theorems (∞,1)-Yoneda lemma (∞,1)-Grothendieck construction adjoint (∞,1)-functor theorem (∞,1)-monadicity theorem Extra stuff, structure, properties Models homotopy theory, (∞,1)-category theory, homotopy type theory flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed… models: topological, simp…

representation, 2-representation, ∞-representation group, ∞-group group algebra, algebraic group, Lie algebra vector space, n-vector space affine space, symplectic vector space action, ∞-action module, equivariant object bimodule, Morita equivalence induced representation, Frobenius reciprocity Hilbert space, Banach space, Fourier transform, functional analysis orbit, coadjoint orbit, Killing for…

In probability theory the expectation value of a random variable or observable is to be thought of as the mean value of that variable/observable under the given probabilities. Taking the concept of expectation value as the primary concept (Whittle 92) develops the theory of probability from axioms on the expectation functional rather than on the axioms of a probability measure. For a measure spac…

Special and general types Special notions Variants Extra structure Operations Theorems This page is to record the reference: John Frank Adams: Stable homotopy and generalized homology Chicago Lectures in Mathematics University of Chicago Press (1974) ISBN:978-0-226-00524-9 ucp:bo21302708 on stable homotopy theory and generalised homology theory, with emphasis on complex cobordism theory, complex …

Special and general types Special notions Variants Extra structure Operations Theorems The universal coefficient theorem states how ordinary homology/ordinary cohomology determines homology/cohomology with arbitrary coefficients. For a chain complex (of abelian groups) and a field (the coefficient field), the homology group and the cohomology group are indeed related by dualization: . If the coef…

A Lorentzian manifold is called globally hyperbolic if it admits a well-defined time evolution from initial data of physical fields on it. There are several equivalent definitions of global hyperbolicity. A simple one is: A Lorentzian manifold (without boundary) is called globally hyperbolic if it contains a Cauchy surface. In this form the characterization of global hyperbolicity appears for ins…

On the global structure and spacetime topology of Kerr-Newman-Reissner-Nordström spacetimes (and making explicit their 2-sphere topology): Brandon Carter: Global Structure of the Kerr Family of Gravitational Fields, Phys. Rev. 174 (1968) 1559 [doi:10.1103/PhysRev.174.1559] (including observation that the gyromagnetic ratio of the Kerr-Newman black hole is 2, just as the for electron cf. at anomal…

This article is about the notion of multiverse in physics. For other notions of multiverse, see multiverse. In physics, the term “multiverse” refers to certain picture of cosmology. The intended meaning tends to differ between authors and/or remain vague (see below) but broadly what goes with it is the idea that, just as the configuration of matter and energy changes from place to place within ou…

Formalism Definition Spacetime configurations Properties Spacetimes Quantum theory (…) Review: Tim Adamo, E. T. Newman, The Kerr-Newman metric: A Review, Scholarpedia 9: 31791 (2014) [arXiv:1410.6626, doi:10.4249/scholarpedia.31791, pdf] Wikipedia, Kerr-Newman metric On the global structure and spacetime topology of Kerr-Newman-Reissner-Nordström spacetimes (and making explicit their 2-sphere top…

On the similarity between Kerr-Newman black holes (charged and spinning “black 0-branes”) and elementary particles (sigma-model 0-branes) like electrons. Historical precursor discussion on the possibility of geometrodynamics for fundamental particles: Seminal observation that the gyromagnetic ratio of the Kerr-Newman black hole is 2, just as the for electron (cf. at anomalous magnetic moment): Br…

Victor Ginzburg (in some 1980s articles spelled Ginsburg) is a professor of mathematics at the University of Chicago. His thesis in Moscow was under Alexandre Kirillov. His main interests are representation theory, especially geometric representation theory, including more recently noncommutative algebraic geometry. Warning: there is another mathematician (global analysis, symplectic geometry), V…

nLab empty 246 Last revised on September 4, 2026 at 20:51:33. See the history of this page for a list of all contributions to it.

You are not a whole. You are not a partial. You are not a nothing. Your presence is fleeting. I can make orders that make you lesser, I can make orders where you dominate. But none of those exist in reality so they are equally meaningless. You cannot be found and yet by inferential ways your limits or your boundaries can be tested, confirmed, and validated. You can, and all that makes you up, and…

On microscopic explanation of Bekenstein-Hawking entropy via geometric engineering of black holes in string theory as bound states of D-branes: Discussion of black hole entropy of D2-D6 brane bound states as black holes in string theory: On D1-D3 brane intersections as spikes/BIons in the D3-brane DBI-theory: On the AdS-CFT correspondence: Juan Maldacena, The Large N limit of superconformal field…

On supersymmetry breaking from super QCD to QCD: On the GSO projection and introducing what came to be called type 0 string theory: On the canonical/geometric quantization of D=3 Chern-Simons theory: Introducing mirror symmetry of D=3 N=4 super Yang-Mills theory: On the D=6 N=(1,0) SCFT on heterotic M5-branes and their KK-compactifications: Discussion of effective non-commutative geometry exhibit…

nLab Appearance Graphs Appearance Graphs by David Ryan "DaemonDave" Erickson? Last revised on September 4, 2026 at 19:06:00. See the history of this page for a list of all contributions to it.

Special and general types Special notions Variants Extra structure Operations Theorems The Atiyah-Hirzebruch spectral sequence (AHSS) is a type of spectral sequence that generalizes the Serre spectral sequence from ordinary cohomology to any generalized (Eilenberg-Steenrod) cohomology theory . For any (finite) homotopy fiber sequence then the corresponding -Atiyah-Hirzebruch spectral sequence has…

Sir Michael Atiyah was a British-Lebanese mathematician, a Fields’ medalist, and Abel prize winner (with Isadore Singer). He was professor of mathematics at Edinburgh University. Wikipedia entry inSpire page MathGenealogy page Memories of Sir Michael Atiyah, Notices of the AMS [pdf, pdf] Bernd Schroers: Michael Atiyah and Physics: the Later Years [arXiv:1910.10630] Alain Connes, Joseph Kouneiher:…

Graeme Bryce Segal On classifying spaces and spectral sequences (and introducing, following Grothendicek 61, the “Segal conditions”, see also at complete Segal space): On the representation rings of compact Lie groups: On the Atiyah-Segal completion theorem: On the proper definition of group cohomology for topological groups: Graeme Segal: Cohomology of topological groups, in: Symposia Mathematic…