nLab
geometry

See also topology.

some of the entries related to geometry

• differential geometry, differential topology, Diff, cobordism

• differential form, tangent space, tangent bundle. cotangent bundle, cotangent complex

• symplectic geometry, symplectic manifold, Poisson manifold, multisymplectic geometry, n-symplectic manifold, foliation, integrable distribution

• fibre bundle, principal bundle, noncommutative principal bundle, vector bundle

• connection (and links therein)

• Morse function, Morse lemma, Morse theory, perfect Morse function

• differentiable stack, orbifold, stratifold, orientifold

• derived algebraic geometry, derived smooth manifold

• noncommutative geometry

• noncommutative algebraic geometry, noncommutative scheme, noncommutative thin scheme

• algebraic geometry, analytic geometry, book entry EGA

• scheme, quasicompact, noetherian scheme, reduced scheme, integral scheme

• open subscheme, closed subscheme, configuration scheme

• formal scheme, formal group scheme, formal group law, algebraic group

• spectrum (geometry)

• algebraic variety, normal variety, Kähler manifold, hyperplane line bundle

• hyperplane section theorem, BBDG decomposition theorem

• algebraic space, algebraic stack, diffiety

• quasicoherent sheaf, coherent sheaf, relative scheme

• smooth scheme, smooth morphism of schemes, etale morphism, formally smooth morphism

• pure motive, Voevodsky motive

• D-module, local system, regular differential operator, Grothendieck connection

• flag variety, geometric quantization, coherent state, orbit, coadjoint orbit

• Lie group, Lie groupoid, Lie algebroid, Courant algebroid

• Lie theory, Lie's three theorems, Erlangen program

• ringed space, ringed site, ringed topos, lined topos

• synthetic differential geometry, infinitesimal object, smooth topos, Kock-Lawvere axiom, infinitesimal singular simplicial complex, differential forms in synthetic differential geometry

  • book entry Models for Smooth Infinitesimal Analysis

• generalized smooth space:

  • Froelicher space, diffeological space, smooth space

• space and quantity

• Euclidean geometry

There are many entries on sheaf, stack, site, locale and topos theory including

• germ, etale space, soft sheaf, flabby sheaf, fine sheaf, Grothendieck topos, Grothendieck topology, (infinity,1)-topos, smooth topos, (infinity,1)-category of (infinity,1)-sheaves, cover, hypercover, local object, local isomorphism, coverage, local epimorphism, hypercompletion, sieve, Verdier site, Grothendieck fibration, Pierce spectrum, Stone duality?, point of a topos, geometric morphism…

and pages on various cohomologies, including sheaf cohomology, nonabelian cohomology, differential cohomology, Deligne cohomology, etale cohomology, equivariant cohomology, Bredon cohomology and their cocycle classes including torsors, gerbes, principal 2-bundles as well as the related picture of the descent theory (cf. oriental, descent for simplicial presheaves…).