• Honam Mathematical Journal
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• v.1 no.1
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• pp.61-75
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• 1979

In this explanation. we shall describle how the de Rham's cohomology on a n-dimensional $C^{**}$-manifold is constructed. The Čech's cohomology defined by only topological structure of $C^{**}$-manifold has a crack that it is dependent on the covering of a $C^{**}$-manifold. At the end of explanation we shall prove that the de Rham's cohomology is isomorphic to Čech's cohomology which is made by simply covering.

• East Asian mathematical journal
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• v.9 no.2
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• pp.295-311
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• 1993

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.1-17
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• 2024

The boundary conditions $\tilde{P}_0$ and $\tilde{P}_1$ were introduced in [5] by using the Hodge decomposition on the de Rham complex. In [6] the Atiyah-Bott-Lefschetz type fixed point formulas were proved on a compact Riemannian manifold with boundary for some special type of smooth functions by using these two boundary conditions. In this paper we slightly extend the result of [6] and give two examples showing these fixed point theorems.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.167-179
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• 1997

In the study of a manifold M, the exterior algebra $\Lambda^* M$ plays an important role. In fact, the de Rham cohomology theory gives many informations of a manifold. Another important object in the study of a manifold is its Clifford algebra (Cl(M), generated by the tangent space.