Jun 03 2024

## Isometry and Homotopy

In Chemistry, “This phenomenon of two or more compounds having the same molecular formula but different structures is called **isomerism**.” ([1], pg. 405) In a positive charge groupoid, traveling through an open gamma ray field, coming from a given nucleus, there is an isometry. Though the homotopy comes across “*an m-dimensionable manifold M of class C ^{r}*” ([2], pg. 646), the gravitons have different phases as the groupoid travels on, in an outer tangent space, and “

*the homotopy problem is equivalent to an extension problem.*” ([3], pg. 175)

“16.2. LEMMA. *If (E,S) is a cell and its boundary, then (E *X* 0)* ꓴ *(S *X* I) is a retract of E *X* I*.” ([3], pg. 84)

Thus, “π is an infinite cyclic group,” ([3], pg. 199). Steenrod calls S “A system S of coordinates” ([3], pg. 22), or “a bundle of coefficients.” ([3], pg. 190) In this case, with “*E *X* I*“, *I* is an isotopy, and the zero space is the tangent space. There is “no left distributive law” ([3], pg. 122), because orbital electrons absorb gravitons at various rates.

It may be that the tangent space is all that the charged particle puts out, and that Lie groups form in the open gamma ray field.

[1] Hein, Morris, “Foundations of College Chemistry, Fourth Edition”, DICKENSON PUBLISHING COMPANY, INC., c. 1977

[2] Whitney, Hassler, “Differential Manifolds”, The Annals of Mathematics, Second Series, Vol. 37. No. 3 (Jul., 1936) pp. 645-680

[3] Steenrod, Norman, “The Topolgy of Fibre Bundles”, Princeton University Press, c. 1951