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- W4385061849 abstract "This paper introduces free group presentations of planar path triangular shapes and their corresponding Betti numbers, introduced by H. Poincaré, inspired by E. Betti’s 1870 work on dimensionality from a computer engineering perspective. In homotopy theory, paths are continuous maps $$h{:},[0,1]rightarrow X$$ from the unit interval to a space X. The edges of path triangles are paths from homotopy theory introduced J. H. C. Whitehead during the late 1940s. The main results in this paper are (1) every path triangle has a J. J. Rotman free group presentation and (2) every path path triangle has a geometric realization as a 1-cycle cell complex." @default.
- W4385061849 created "2023-07-23" @default.
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- W4385061849 date "2023-01-01" @default.
- W4385061849 modified "2023-10-18" @default.
- W4385061849 title "Free Group Presentation of Triangular Planar Shapes and Their Betti Numbers: Computer Engineering Perspective" @default.
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- W4385061849 doi "https://doi.org/10.1007/978-981-19-8054-1_24" @default.
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