This is a glossary of properties and concepts in
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
in mathematics.
See also:
glossary of topology
This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fund ...
,
list of algebraic topology topics
This is a list of algebraic topology topics, by Wikipedia page. See also:
* Glossary of algebraic topology
*topology glossary
* List of topology topics
* List of general topology topics
*List of geometric topology topics
* Publications in topology
...
,
glossary of category theory
This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.)
*Notes on foundations: In many expositions (e.g., Vistoli), the set-theoretic issues are ignored; this means, for instance, t ...
,
glossary of differential geometry and topology
This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related:
*Glossary of general topology
*Glossary of algebraic topology
*Glossary of Riemannian and metric geometr ...
,
Timeline of manifolds.
*Convention: Throughout the article, ''I'' denotes the unit interval, ''S''
''n'' the
''n''-sphere and ''D''
''n'' the ''n''-disk. Also, throughout the article, spaces are assumed to be reasonable; this can be taken to mean for example, a space is a CW complex or
compactly generated In mathematics, compactly generated can refer to:
* Compactly generated group, a topological group which is algebraically generated by one of its compact subsets
*Compactly generated space
In topology, a compactly generated space is a topological s ...
weakly Hausdorff space. Similarly, no attempt is made to be definitive about the definition of a
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
. A
simplicial set
In mathematics, a simplicial set is an object composed of ''simplices'' in a specific way. Simplicial sets are higher-dimensional generalizations of directed graphs, partially ordered sets and categories. Formally, a simplicial set may be defined a ...
is not thought of as a space; i.e., we generally distinguish between simplicial sets and their geometric realizations.
*Inclusion criterion: As there is no
glossary of homological algebra in Wikipedia right now, this glossary also includes a few concepts in homological algebra (e.g., chain homotopy); some concepts in
geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
History
Geometric topology as an area distinct from algebraic topology may be said to have originated i ...
and
differential topology
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...
are also fair game. On the other hand, the items that appear in
glossary of topology
This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fund ...
are generally omitted.
Abstract homotopy theory and
motivic homotopy theory
In music, a motif IPA: ( /moʊˈtiːf/) (also motive) is a short musical phrase, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition: "The motive ...
are also outside the scope.
Glossary of category theory
This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.)
*Notes on foundations: In many expositions (e.g., Vistoli), the set-theoretic issues are ignored; this means, for instance, t ...
covers (or will cover) concepts in theory of
model categories. See the
glossary of symplectic geometry
This is a glossary of properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over the complex numbers for definiteness). T ...
for the topics in symplectic topology such as quantization.
!$@
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Notes
References
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* Lectures delivered by Michael Hopkins and Notes by Akhil Mathew, Harvard.
*
*
*
*
* (despite the title, it contains a significant amount of general results.)
*
* the 1970 MIT notes
*
*{{cite web , first=Kirsten Graham , last=Wickelgren , authorlink=Kirsten Wickelgren, url=http://people.math.gatech.edu/~kwickelgren3/8803_Stable/ , title=8803 Stable Homotopy Theory
Further reading
* José I. Burgos Gil
The Regulators of Beilinson and BorelLectures on groups of homotopy spheresby JP Levine
External links
Algebraic Topology: A guide to literature
Algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
Wikipedia glossaries using description lists