The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians
For F=R, C, or H, let GkFn denote the Grassmannian of k-planes in Fn. For a well-known Morse function f:GkFn⟶R, we denote by Cf the fiber product of two copies of f. We prove a formula which describes χCf.
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/8418617 |
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| _version_ | 1849223062516400128 |
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| author | Yasuhiko Kamiyama |
| author_facet | Yasuhiko Kamiyama |
| author_sort | Yasuhiko Kamiyama |
| collection | DOAJ |
| description | For F=R, C, or H, let GkFn denote the Grassmannian of k-planes in Fn. For a well-known Morse function f:GkFn⟶R, we denote by Cf the fiber product of two copies of f. We prove a formula which describes χCf. |
| format | Article |
| id | doaj-art-0aeb0d11a2034c378e1e8159ee40ec3c |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0aeb0d11a2034c378e1e8159ee40ec3c2025-08-26T00:00:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/8418617The Euler Characteristic of the Fiber Product of Morse Functions on GrassmanniansYasuhiko Kamiyama0Department of Mathematical SciencesFor F=R, C, or H, let GkFn denote the Grassmannian of k-planes in Fn. For a well-known Morse function f:GkFn⟶R, we denote by Cf the fiber product of two copies of f. We prove a formula which describes χCf.http://dx.doi.org/10.1155/ijmm/8418617 |
| spellingShingle | Yasuhiko Kamiyama The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians International Journal of Mathematics and Mathematical Sciences |
| title | The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians |
| title_full | The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians |
| title_fullStr | The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians |
| title_full_unstemmed | The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians |
| title_short | The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians |
| title_sort | euler characteristic of the fiber product of morse functions on grassmannians |
| url | http://dx.doi.org/10.1155/ijmm/8418617 |
| work_keys_str_mv | AT yasuhikokamiyama theeulercharacteristicofthefiberproductofmorsefunctionsongrassmannians AT yasuhikokamiyama eulercharacteristicofthefiberproductofmorsefunctionsongrassmannians |