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| dc.contributor.supervisor | Gatsinzi, Jean Baptiste | |
| dc.contributor.author | Maphane, Oteng | |
| dc.date.accessioned | 2023-02-02T09:08:04Z | |
| dc.date.available | 2023-02-02T09:08:04Z | |
| dc.date.issued | 2022-05-04 | |
| dc.identifier.citation | Maphane, O. (2022) Loop space homology of elliptic spaces, PhD Dissertation, Botswana International University of Science and Technology: Palapye. | en_US |
| dc.identifier.uri | http://repository.biust.ac.bw/handle/123456789/529 | |
| dc.description.abstract | In this thesis, we use the theory of minimal Sullivan models in rational homotopy theory to study the partial computation of the Lie bracket structure of the string homology on a formal elliptic space. In the process, we show the total space of the unit sphere tangent bundleS2m−1 → Ep→ Gk,n(C) over complex Grassmannian manifolds Gk,n(C) for 2 ≤ k ≤ n/2, where m = k(n − k) is not formal. This is done by exhibiting a non trivial Massey triple product. On the other hand, let φ :(∧V,d) → (B,d) be a surjective morphism between com mutative differential graded algebras, where V is finite dimensional, and consider (B,d) a module over ∧V via the mapping φ. We show that the Hochschild cohomology HH∗ (∧V;B) can be computed in terms of the graded vector space of positive φ-derivations. Given a Koszul Sullivan extension (∧V,d) f ↣ (∧V ⊗ ∧W,d) = (C,d), we show that if (∧V,d) is an elliptic 2-stage Postnikov tower Sullivan algebra, and if the natural homo morphism of the differential graded algebras (C,d) → (∧W,d¯) is surjective in homology, then the natural graded linear map HH∗ (f) : HH∗ (∧V;∧V) → HH∗ (∧V;C), induced in Hochschild cohomology by the inclusion (∧V,d) f ↣ (C,d), is injective. In particular, if X is an elliptic 2-stage Postnikov tower, and (∧V,d) is the minimal Sullivan model of X, then HH∗ (f) : H∗(X S 1 ;Q) → HH∗ (∧V;C) is injective, where X S 1 is the space of free loops on X, and H∗(X S 1 ;Q) is the loop space homology. | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Botswana International University of Science and Technology (BIUST) | en_US |
| dc.subject | Minimal Sullivan models | en_US |
| dc.subject | Hochschild cohomology HH∗ (∧V;B) | en_US |
| dc.subject | Elliptic space | en_US |
| dc.subject | Non trivial Massey triple product. | en_US |
| dc.title | Loop space homology of elliptic spaces | en_US |
| dc.description.level | phd | en_US |
| dc.dc.description | Dissertation (Doctor of Philosophy in Pure and Applied Mathematics )---Botswana International University of Science and Technology, 2022 | |
| dc.description.accessibility | unrestricted | en_US |
| dc.description.department | mss | en_US |
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