oriented homology group

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• Homology sphere — In algebraic topology, a homology sphere is an n manifold X having the homology groups of an n sphere, for some integer n ≥ 1. That is, we have: H 0( X ,Z) = Z = H n ( X ,Z)and : H i ( X ,Z) = {0} for all other i .Therefore X is a connected space …   Wikipedia

• Homology theory — In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces. Simple explanation At the… …   Wikipedia

• Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… …   Wikipedia

• Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are …   Wikipedia

• Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

• Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia

• Intersection homology — In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them… …   Wikipedia

• Morse homology — In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be… …   Wikipedia

• Cobordism — A cobordism (W;M,N). In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint… …   Wikipedia

• Seifert fiber space — A Seifert fiber space is a 3 manifold together with a nice decomposition as a disjoint union of circles. In other words it is a S^1 bundle (circle bundle) over a 2 dimensional orbifold. Most small 3 manifolds are Seifert fiber spaces, and they… …   Wikipedia

• Orientability — For orientation of vector spaces, see orientation (mathematics). For other uses, see Orientation (disambiguation). The torus is an orientable surface …   Wikipedia