Cohomology Theories for Compact Abelian Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two |
| Beschreibung: | 1 Online-Ressource (236 p) |
| ISBN: | 9783642806704 9783642806728 |
| DOI: | 10.1007/978-3-642-80670-4 |
Internformat
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| 245 | 1 | 0 | |a Cohomology Theories for Compact Abelian Groups |c by Karl H. Hofmann, Paul S. Mostert |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1973 | |
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| 500 | |a Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two | ||
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Datensatz im Suchindex
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| author | Hofmann, Karl H. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-80670-4 |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642806704 9783642806728 |
| language | English |
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| spelling | Hofmann, Karl H. Verfasser aut Cohomology Theories for Compact Abelian Groups by Karl H. Hofmann, Paul S. Mostert Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (236 p) txt rdacontent c rdamedia cr rdacarrier Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two Mathematics Mathematics, general Mathematik Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Kompakte Gruppe (DE-588)4164840-7 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Kompakte Gruppe (DE-588)4164840-7 s Kohomologietheorie (DE-588)4164610-1 s 1\p DE-604 Abelsche Gruppe (DE-588)4140988-7 s Kohomologie (DE-588)4031700-6 s 2\p DE-604 Mostert, Paul S. Sonstige oth https://doi.org/10.1007/978-3-642-80670-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hofmann, Karl H. Cohomology Theories for Compact Abelian Groups Mathematics Mathematics, general Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Kohomologie (DE-588)4031700-6 gnd Kompakte Gruppe (DE-588)4164840-7 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4031700-6 (DE-588)4164840-7 (DE-588)4140988-7 |
| title | Cohomology Theories for Compact Abelian Groups |
| title_auth | Cohomology Theories for Compact Abelian Groups |
| title_exact_search | Cohomology Theories for Compact Abelian Groups |
| title_full | Cohomology Theories for Compact Abelian Groups by Karl H. Hofmann, Paul S. Mostert |
| title_fullStr | Cohomology Theories for Compact Abelian Groups by Karl H. Hofmann, Paul S. Mostert |
| title_full_unstemmed | Cohomology Theories for Compact Abelian Groups by Karl H. Hofmann, Paul S. Mostert |
| title_short | Cohomology Theories for Compact Abelian Groups |
| title_sort | cohomology theories for compact abelian groups |
| topic | Mathematics Mathematics, general Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Kohomologie (DE-588)4031700-6 gnd Kompakte Gruppe (DE-588)4164840-7 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Kohomologietheorie Kohomologie Kompakte Gruppe Abelsche Gruppe |
| url | https://doi.org/10.1007/978-3-642-80670-4 |
| work_keys_str_mv | AT hofmannkarlh cohomologytheoriesforcompactabeliangroups AT mostertpauls cohomologytheoriesforcompactabeliangroups |