Geometry of configurations in tangent groups
This article relates the Grassmannian complexes of geometric configurations to the tangent to the Bloch-Suslin complex and to the tangent to Goncharov’s motivic complex. By means of morphisms, we bring the geometry of configurations in tangent groups, $T\mathcal{B}_2(F)$ and $T\mathcal{B}_3(F)$ that...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020035/fulltext.html |
| _version_ | 1811277631367151616 |
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| author | Raziuddin Siddiqui |
| author_facet | Raziuddin Siddiqui |
| author_sort | Raziuddin Siddiqui |
| collection | DOAJ |
| description | This article relates the Grassmannian complexes of geometric configurations to the tangent to the Bloch-Suslin complex and to the tangent to Goncharov’s motivic complex. By means of morphisms, we bring the geometry of configurations in tangent groups, $T\mathcal{B}_2(F)$ and $T\mathcal{B}_3(F)$ that produce commutative diagrams. To show the commutativity of diagrams, we use combinatorial techniques that include permutations in symmetric group <em>S</em><sub>6</sub>. We also create analogues of the Siegel’s cross-ratio identity for the truncated polynomial ring <em>F</em>[<em>ε</em>]<sub><em>ν</em></sub>. |
| first_indexed | 2024-04-13T00:20:20Z |
| format | Article |
| id | doaj.art-8ef27c7f10b74440aea486d7d359bf07 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T00:20:20Z |
| publishDate | 2020-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-8ef27c7f10b74440aea486d7d359bf072022-12-22T03:10:48ZengAIMS PressAIMS Mathematics2473-69882020-01-015152254510.3934/math.2020035Geometry of configurations in tangent groupsRaziuddin Siddiqui0Department of Mathematical Sciences, Institute of Business Administration, Karachi, PakistanThis article relates the Grassmannian complexes of geometric configurations to the tangent to the Bloch-Suslin complex and to the tangent to Goncharov’s motivic complex. By means of morphisms, we bring the geometry of configurations in tangent groups, $T\mathcal{B}_2(F)$ and $T\mathcal{B}_3(F)$ that produce commutative diagrams. To show the commutativity of diagrams, we use combinatorial techniques that include permutations in symmetric group <em>S</em><sub>6</sub>. We also create analogues of the Siegel’s cross-ratio identity for the truncated polynomial ring <em>F</em>[<em>ε</em>]<sub><em>ν</em></sub>.https://www.aimspress.com/article/10.3934/math.2020035/fulltext.htmlaffine spacescross-ratiotangent complexodd permutationsymmetric group |
| spellingShingle | Raziuddin Siddiqui Geometry of configurations in tangent groups AIMS Mathematics affine spaces cross-ratio tangent complex odd permutation symmetric group |
| title | Geometry of configurations in tangent groups |
| title_full | Geometry of configurations in tangent groups |
| title_fullStr | Geometry of configurations in tangent groups |
| title_full_unstemmed | Geometry of configurations in tangent groups |
| title_short | Geometry of configurations in tangent groups |
| title_sort | geometry of configurations in tangent groups |
| topic | affine spaces cross-ratio tangent complex odd permutation symmetric group |
| url | https://www.aimspress.com/article/10.3934/math.2020035/fulltext.html |
| work_keys_str_mv | AT raziuddinsiddiqui geometryofconfigurationsintangentgroups |