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Meaning of "cohomology" in the English dictionary

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DICTIONARY
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PRONUNCIATION OF COHOMOLOGY

cohomology  [ˌkəʊhəˈmɒlədʒɪ] play
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GRAMMATICAL CATEGORY OF COHOMOLOGY

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Cohomology is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES COHOMOLOGY MEAN IN ENGLISH?

Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign 'quantities' to the chains of homology theory. From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century; from the initial idea of homology as a topologically invariant relation on chains, the range of applications of homology and cohomology theories has spread out over geometry and abstract algebra. The terminology tends to mask the fact that in many applications cohomology, a contravariant theory, is more natural than homology.

Definition of cohomology in the English dictionary

The definition of cohomology in the dictionary is the abstract study of algebraic topology.

WORDS THAT RHYME WITH COHOMOLOGY


anemology
ˌænɪˈmɒlədʒɪ
atmology
ætˈmɒlədʒɪ
cosmology
kɒzˈmɒlədʒɪ
docimology
ˌdɒsɪˈmɒlədʒɪ
entomology
ˌɛntəˈmɒlədʒɪ
enzymology
ˌɛnzaɪˈmɒlədʒɪ
epistemology
ɪˌpɪstɪˈmɒlədʒɪ
etymology
ˌɛtɪˈmɒlədʒɪ
gemmology
dʒɛˈmɒlədʒɪ
gemology
dʒɛˈmɒlədʒɪ
gizmology
ɡɪzˈmɒlədʒɪ
homology
həʊˈmɒlədʒɪ
ophthalmology
ˌɒfθælˈmɒlədʒɪ
orismology
ˌɒrɪzˈmɒlədʒɪ
pomology
pɒˈmɒlədʒɪ
potamology
ˌpɒtəˈmɒlədʒɪ
seismology
saɪzˈmɒlədʒɪ
sphygmology
sfɪɡˈmɒlədʒɪ
victimology
ˌvɪktɪˈmɒlədʒɪ
zymology
zaɪˈmɒlədʒɪ

WORDS THAT BEGIN LIKE COHOMOLOGY

cohesively
cohesiveness
cohibit
cohibition
cohibitive
coho
cohobate
cohog
coholder
cohomological
cohort
cohortative
cohosh
cohost
cohostess
cohousing
COHSE
cohune
cohune palm
cohyponym

WORDS THAT END LIKE COHOMOLOGY

archaeology
astrology
biology
biotechnology
ecology
genealogy
geology
information technology
methodology
microbiology
mythology
neurology
oncology
pathology
pharmacology
physiology
psychology
sociology
technology
terminology
theology

Synonyms and antonyms of cohomology in the English dictionary of synonyms

SYNONYMS

Translation of «cohomology» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF COHOMOLOGY

Find out the translation of cohomology to 25 languages with our English multilingual translator.
The translations of cohomology from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «cohomology» in English.

Translator English - Chinese

上同调
1,325 millions of speakers

Translator English - Spanish

cohomología
570 millions of speakers

English

cohomology
510 millions of speakers

Translator English - Hindi

cohomology
380 millions of speakers
ar

Translator English - Arabic

كهومولوج)
280 millions of speakers

Translator English - Russian

когомологий
278 millions of speakers

Translator English - Portuguese

cohomology
270 millions of speakers

Translator English - Bengali

cohomology
260 millions of speakers

Translator English - French

cohomologie
220 millions of speakers

Translator English - Malay

Kohomologi
190 millions of speakers

Translator English - German

Kohomologie
180 millions of speakers

Translator English - Japanese

コホモロジー
130 millions of speakers

Translator English - Korean

코호 몰 로지
85 millions of speakers

Translator English - Javanese

Cohomology
85 millions of speakers
vi

Translator English - Vietnamese

đối đồng điều
80 millions of speakers

Translator English - Tamil

cohomology
75 millions of speakers

Translator English - Marathi

Cohomology
75 millions of speakers

Translator English - Turkish

cohomoloji
70 millions of speakers

Translator English - Italian

coomologia
65 millions of speakers

Translator English - Polish

cohomology
50 millions of speakers

Translator English - Ukrainian

когомологій
40 millions of speakers

Translator English - Romanian

coomologie
30 millions of speakers
el

Translator English - Greek

cohomology
15 millions of speakers
af

Translator English - Afrikaans

cohomologie
14 millions of speakers
sv

Translator English - Swedish

Snittkohomologi
10 millions of speakers
no

Translator English - Norwegian

kohomologien
5 millions of speakers

Trends of use of cohomology

TRENDS

TENDENCIES OF USE OF THE TERM «COHOMOLOGY»

The term «cohomology» is regularly used and occupies the 108.150 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Regularly used
50
/100
The map shown above gives the frequency of use of the term «cohomology» in the different countries.
Principal search tendencies and common uses of cohomology
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «cohomology».

FREQUENCY OF USE OF THE TERM «COHOMOLOGY» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «cohomology» during the past 500 years. Its implementation is based on analysing how often the term «cohomology» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about cohomology

EXAMPLES

10 ENGLISH BOOKS RELATING TO «COHOMOLOGY»

Discover the use of cohomology in the following bibliographical selection. Books relating to cohomology and brief extracts from same to provide context of its use in English literature.
1
From Calculus to Cohomology: De Rham Cohomology and ...
An introductory textbook on cohomology and curvature with emphasis on applications.
Ib H. Madsen, Jxrgen Tornehave, 1997
2
Galois Cohomology
This book is an updated English translation of an influential work Cohomologie Galoisienne, published more than 30 years ago.
Jean-Pierre Serre, 2002
3
Cohomology of Groups
As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites.
Kenneth S. Brown, 1982
4
Representations and Cohomology: Volume 1, Basic ...
This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules.
D. J. Benson, 1998
5
Cohomology of Finite Groups
Some Historical Background This book deals with the cohomology of groups, particularly finite ones.
Alejandro Adem, R. James Milgram, 2004
6
Continuous Cohomology, Discrete Subgroups, and ...
In the years since the first edition of this work, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups.
Armand Borel, Nolan R. Wallach, 2000
7
Secondary Cohomology Operations
Starting with a CW pair, we observe that the q-th cohomology of the pair maps monomorphically into the q-th cohomology of the q-skeleton of the pair. By naturality, this composition factors through 0. For arbitrary pairs, the result follows by use ...
John R. Harper, 2002
8
Lie Groups, Lie Algebras, and Cohomology
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group ...
Anthony W. Knapp, 1988
9
Cohomology of Number Fields
The Galois groups G = G(L|K) of Galois extensions L|K are profinite groups and we may such use cohomology theory which we have developed in the preceding chapters. We are particularly interested in the meaning of the cohomology ...
Jürgen Neukirch, Alexander Schmidt, Kay Wingberg, 2013
10
Generalized Cohomology
This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Akira Kōno, 2006

10 NEWS ITEMS WHICH INCLUDE THE TERM «COHOMOLOGY»

Find out what the national and international press are talking about and how the term cohomology is used in the context of the following news items.
1
Quantum Hamiltonian complexity: Worth the wait
... completion of the full classification of phases in one-dimensional gapped spin chains in terms of the so-called second cohomology group. «Nature.com, Jul 15»
2
2015 Marker Lectures in the Mathematical Sciences Scheduled for …
... of Mathematics at the University of Michigan, he established a mathematical theory for quantum cohomology and Gromov-Witten invariants. «PressZoom, Mar 15»
3
Breakthrough Prize Awards: Like A Celeb Bash, Except These …
... classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology. «Huffington Post UK, Nov 14»
4
A Billionaire Mathematician's Life of Ferocious Curiosity
In 2007, the resulting paper ran under the title “Axiomatic Characterization of Ordinary Differential Cohomology.” What? “It's very hard to explain ... «New York Times, Jul 14»
5
The $3m prize for maths? Welcome to the X2+y2 factor
... "elliptical cohomology" and "combinatorics". As part of the deal, all the winners have agreed to sit on the selection committee for subsequent ... «The Independent, Jun 14»
6
Silicon Valley Giants Hand Out $15 Million In Prizes To …
... classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology. «Gizmodo Australia, Jun 14»
7
King Faisal award honor for scholars
His deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on ... «Arab News, Mar 14»
8
Winners of KING FAISAL INTERNATIONAL PRIZE 2014
His deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on ... «The Nation, Feb 14»
9
Saudi scholar wins Faisal Prize for Islamic Studies
His deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on ... «Saudi Gazette, Jan 14»
10
Belgian Mathematician Wins Abel Prize for Shaping Algebraic …
Grothendieck laid the foundations for finding the right cohomology, but his student Deligne found the final proof alone — and in a different way ... «Scientific American, Mar 13»

REFERENCE
« EDUCALINGO. Cohomology [online]. Available <https://educalingo.com/en/dic-en/cohomology>. May 2024 ».
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