Author(s)

Huang Juhui ^1,2

Affiliation(s)

¹ Guilin Institute of Information Technology, Guilin, Guangxi, China
² Baise University, Baise, Guangxi, China

Corresponding Author

Huang Juhui

ABSTRACT

Triangular prism is a common geometric shape. From the perspective of algebraic topology, it is a familiar simple convex polyhedron in algebraic topology. In this paper, we mainly calculate that there are only two kinds of characteristic functions on a triangular prism, and the homology groups of triangular prism is obtained by different characteristic functions are different. Firstly, according to the Morse function on the convex polytope Pⁿ, We can give the cell decoposition of the corresponding small cover Mⁿ over Pⁿ, and the cellular chain complex {D_i(Mⁿ(λ)),∂_i} of Mⁿ. Secondly, considering the relationship between the boundary homomorphism {∂_i} and the characteristic function λ, we can give the principle of how to determine the boundary homomorphism is given. Finally, the homology groups are computed by defination {H_i= ker∂_i / Im∂_i+1}, we can give the corresponding results.

KEYWORDS

Small cover, the homology group, triangular prism

CITE THIS PAPER

Huang Juhui, The homology groups of small cover on a triangular prism and its number of characteristic functions. Transactions on Computational and Applied Mathematics (2023) Vol. 3: 26-32. DOI: http://dx.doi.org/10.23977/tracam.2023.030104.

REFERENCES

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[5] Choi S. (2008) The number of small covers over cubes. Algebraic and Geometric Topology, 8, 2391-2399. 
[6] Liu Dengpin. The characteristic function of  and Moment-Angle manifold of Partial-quotient [D]: [PhD dissertation]. Shanghai: Department of Mathematics, Fudan University, 2012. 
[7] Fu Xin. The small cover on the L bell polyhedron [D]: [Master's thesis]. Shanghai: Department of Mathematics, Fudan University, 2013. 
[8] Hao Peide. The cohomology rigidity problem of the small cover on the L bell polyhedron and [D]: [Master's thesis]. Shanghai: Department of Mathematics, Fudan University, 2013. 
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