topology and geometry

* **mathematics**
* math resources
* history of mathematics
* Structural Foundations
* logic
* internal language
* classical mathematics
* evil
* constructive mathematics
* predicative mathematics
* [category:foundational axiom](http://ncatlab.org/nlab/list/foundational+axiom)
* set theory
* structural set theory
* category theory
* Categories and Sheaves
* topos theory
* Sheaves in Geometry and Logic
* higher category theory
* higher topos theory
* (∞,1)-topos theory
* models for ∞-stack (∞,1)-toposes
* cohomology
* homotopy theory
* stable homotopy theory
* rational homotopy theory
* Topology and Geometry
* geometry (general list), topology (general list)
* general topology
* differential topology
* differential geometry
* synthetic differential geometry
* symplectic geometry
* algebraic geometry
* noncommutative algebraic geometry
* noncommutative geometry (general flavour)
* higher geometry
* Algebra
* universal algebra
* higher algebra
* homological algebra
* group theory, ring theory
* representation theory
* algebraic approaches to differential calculus
* counterexamples in algebra
* analysis
* nonstandard analysis
* functional analysis
* operator algebras
* Fourier transform
* Lie theory
* higher Lie theory
* probability theory
* discrete mathematics

up: Mathematics

Some of the subfields of topology and geometry touched in the nlab: general topology, homotopy theory, rational homotopy theory, differential geometry (including symplectic geometry, synthetic differential geometry), differential topology, algebraic geometry, noncommutative algebraic geometry, noncommutative geometry.

Nowdays however there exist many frameworks in which in a unified way, the main objects (kinds of spaces, like schemes or supermanifolds) in several of the above categories can be obtained, for example ringed space, ringed site, structured (infinity,1)-topos…

Here are some nonexhaustive but longer grouped-lists of entries: geometry, topology.

Revised on July 15, 2010 13:26:54
by David Corfield
(86.152.177.227)