Homology theory

general way of associating a sequence of algebraic objects to other mathematical objects

conjecture in algebraic geometry that every Hodge class on a nonsingular complex projective manifold is a linear combination with rational coefficients of the cohomology classes of complex subvarieties

homology of the chain complex of singular chains (integer linear combinations of maps from simplexes into a given topological space)

long exact sequence describing how the (co)homology of a space relates to that of two subspaces whose interiors cover the total space

duality that relates homology and cohomology groups for oriented closed manifolds

theorem that relates homotopy groups to homology groups

analysis of datasets using techniques from topology

secondary characteristic class defined for odd-dimensional manifolds with G-bundles with connection; in 2n−1 dimensions, defined as (formal) exterior antiderivative of tr(Fⁿ) where F is the curvature of the connection

symplectic topology tool

topological manifold whose homology coincides with that of a sphere, i.e. trivial except in the top and bottom degrees, where it has a single generator

method of adjoining two cocycles to form a composite cocycle

properties that homology theories of topological spaces have in common

method for computing topological features of a space at different spatial resolutions

mathematical theorem

method of adjoining a chain of with a cochain

concept in topology

Cohomology class of topological structures