The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians

Yasuhiko Kamiyama

doi:10.1155/ijmm/8418617

January 1, 2025International Journal of Mathematics and Mathematical SciencesOpen Access

The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians

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Key Points

The formula describes the euler characteristic of the fiber product of two Morse functions, providing key insights into their properties.
Specifically, it characterizes χ(C(f)), revealing the underlying structure of fiber products generated by Morse functions.
This analysis employs advanced mathematical concepts such as grassmannians and fiber products, essential in topology studies.
Understanding these relationships helps to deepen knowledge in topology, particularly regarding Morse theory and grassmannians.

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Implication

Analysis of the euler characteristic reveals its relationship to fiber products in grassmannians, suggesting new insights in topology.

Abstract

For , , or , let denote the Grassmannian of k ‐planes in . For a well‐known Morse function , we denote by C ( f ) the fiber product of two copies of f . We prove a formula which describes χ ( C ( f )).

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Yasuhiko Kamiyama (2025) studied this question.

synapsesocial.com/papers/68af4546ad7bf08b1ead2fe1 https://doi.org/10.1155/ijmm/8418617

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The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians

Key Points

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Implication

Abstract

Discussion

Cite This Study

The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians

Key Points

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Implication

Abstract

Discussion

Cite This Study

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