Homological properties of cochain Differential Graded algebras
Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap Theorem. Thes...
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creator | Frankild, Anders J Jorgensen, Peter |
description | Consider a local chain Differential Graded algebra, such as the singular
chain complex of a pathwise connected topological group.
In two previous papers, a number of homological results were proved for such
an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap
Theorem. These were inspired by homological ring theory.
By the so-called looking glass principle, one would expect that analogous
results exist for simply connected cochain Differential Graded algebras, such
as the singular cochain complex of a simply connected topological space.
Indeed, this paper establishes such analogous results. |
doi_str_mv | 10.48550/arxiv.0801.1581 |
format | Article |
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chain complex of a pathwise connected topological group.
In two previous papers, a number of homological results were proved for such
an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap
Theorem. These were inspired by homological ring theory.
By the so-called looking glass principle, one would expect that analogous
results exist for simply connected cochain Differential Graded algebras, such
as the singular cochain complex of a simply connected topological space.
Indeed, this paper establishes such analogous results.</description><identifier>DOI: 10.48550/arxiv.0801.1581</identifier><language>eng</language><subject>Mathematics - K-Theory and Homology ; Mathematics - Rings and Algebras</subject><creationdate>2008-01</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/0801.1581$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0801.1581$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Frankild, Anders J</creatorcontrib><creatorcontrib>Jorgensen, Peter</creatorcontrib><title>Homological properties of cochain Differential Graded algebras</title><description>Consider a local chain Differential Graded algebra, such as the singular
chain complex of a pathwise connected topological group.
In two previous papers, a number of homological results were proved for such
an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap
Theorem. These were inspired by homological ring theory.
By the so-called looking glass principle, one would expect that analogous
results exist for simply connected cochain Differential Graded algebras, such
as the singular cochain complex of a simply connected topological space.
Indeed, this paper establishes such analogous results.</description><subject>Mathematics - K-Theory and Homology</subject><subject>Mathematics - Rings and Algebras</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb0woJadCfkHEvzivNReKqEWWqRKLN2j52e7tZTWkVOh8vdQYDrL1dE9QjyCqluDqJ6pXNNnrYyCGtDAvVhu8ykP-ZCYBjmWPIZySWGSOUrOfKR0lusUYyjhfEk_k00hH7yk4RBcoWku7iINU3j450zs3173q221-9i8r152FXUIlfYWFSkDxEiamqiRfWjBRge2I91oYFzYFo1iG5uWyZFzznPH2jfW6Zl4-tP-_u_Hkk5UvvpbR3_r0N9EVkNx</recordid><startdate>20080110</startdate><enddate>20080110</enddate><creator>Frankild, Anders J</creator><creator>Jorgensen, Peter</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20080110</creationdate><title>Homological properties of cochain Differential Graded algebras</title><author>Frankild, Anders J ; Jorgensen, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a651-3d950a081ac5a3a2f35cde419fb196a3231c5794580c9f24cababbbdc6c3d29b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Mathematics - K-Theory and Homology</topic><topic>Mathematics - Rings and Algebras</topic><toplevel>online_resources</toplevel><creatorcontrib>Frankild, Anders J</creatorcontrib><creatorcontrib>Jorgensen, Peter</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Frankild, Anders J</au><au>Jorgensen, Peter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Homological properties of cochain Differential Graded algebras</atitle><date>2008-01-10</date><risdate>2008</risdate><abstract>Consider a local chain Differential Graded algebra, such as the singular
chain complex of a pathwise connected topological group.
In two previous papers, a number of homological results were proved for such
an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap
Theorem. These were inspired by homological ring theory.
By the so-called looking glass principle, one would expect that analogous
results exist for simply connected cochain Differential Graded algebras, such
as the singular cochain complex of a simply connected topological space.
Indeed, this paper establishes such analogous results.</abstract><doi>10.48550/arxiv.0801.1581</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - K-Theory and Homology Mathematics - Rings and Algebras |
title | Homological properties of cochain Differential Graded algebras |
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