Computations of Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7

We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and cohomology operations, we compute explicit generators for the Spin-$G$ bordism groups in dimensions up to 7.

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Publication Details

Journal
ArXiv.org
Published
2025-04-21
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Computations of Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

Computations of Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7

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Abstract

We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and cohomology operations, we compute explicit generators for the Spin-$G$ bordism groups in dimensions up to 7.

ArXiv.org
Meguro Parasitological Museum (JP), The University of Tokyo (JP)
Openalex Percentile: Top 44%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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Computations of Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7 · ArXiv.org (2025) | TGRS Research Map | TGRS