The Gromov-Lawson-Rosenberg Conjecture for Z/4xZ/4
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910566284525568 |
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| author | Barcenas, Noe Garcia-Hernandez, Luis Eduardo Reinauer, Raphael |
| author_facet | Barcenas, Noe Garcia-Hernandez, Luis Eduardo Reinauer, Raphael |
| contents | We prove the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4 by computing the connective real k-homology of the classifying space with the Adams spectral sequence and two types of detection theorems for the kernel of the alpha invariant: one based on eta-invariants, closely following work of Botvinnik-Gilkey-Stolz, and a second one based on homological methods. Along the way, we determine differentials of the Adams spectral sequence for classifying spaces involved in the computation, and we study the cap structure of the Adams spectral sequence for sub-hopf algebras of the Steenrod algebra relevant to the computation of connective real and complex k-homology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_07895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gromov-Lawson-Rosenberg Conjecture for Z/4xZ/4 Barcenas, Noe Garcia-Hernandez, Luis Eduardo Reinauer, Raphael Algebraic Topology Differential Geometry K-Theory and Homology 19L41, 53C21 We prove the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4 by computing the connective real k-homology of the classifying space with the Adams spectral sequence and two types of detection theorems for the kernel of the alpha invariant: one based on eta-invariants, closely following work of Botvinnik-Gilkey-Stolz, and a second one based on homological methods. Along the way, we determine differentials of the Adams spectral sequence for classifying spaces involved in the computation, and we study the cap structure of the Adams spectral sequence for sub-hopf algebras of the Steenrod algebra relevant to the computation of connective real and complex k-homology. |
| title | The Gromov-Lawson-Rosenberg Conjecture for Z/4xZ/4 |
| topic | Algebraic Topology Differential Geometry K-Theory and Homology 19L41, 53C21 |
| url | https://arxiv.org/abs/2408.07895 |