{"id":1093,"date":"2024-06-03T08:03:49","date_gmt":"2024-06-03T13:03:49","guid":{"rendered":"https:\/\/www.fruechtetheory.com\/blog\/?p=1093"},"modified":"2024-06-03T08:04:54","modified_gmt":"2024-06-03T13:04:54","slug":"isometry-and-homotopy","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2024\/06\/03\/isometry-and-homotopy\/","title":{"rendered":"Isometry and Homotopy"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In Chemistry, \u201cThis phenomenon of two or more compounds having the same molecular formula but different structures is called <strong>isomerism<\/strong>.\u201d ([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 \u201c<em>an m-dimensionable manifold M of class C<sup>r<\/sup><\/em>\u201d ([2], pg. 646), the gravitons have different phases as the groupoid travels on, in an outer tangent space, and \u201c<em>the homotopy problem is equivalent to an extension problem.<\/em>\u201d ([3], pg. 175)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201c16.2. LEMMA.&nbsp; <em>If (E,S) is a cell and its boundary, then (E <\/em>X<em> 0)<\/em> \ua4f4 <em>(S <\/em>X<em> I) is a retract of E <\/em>X<em> I<\/em>.\u201d ([3], pg. 84)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, \u201c\u03c0 is an infinite cyclic group,\u201d ([3], pg. 199). Steenrod calls S \u201cA system S of coordinates\u201d ([3], pg. 22), or \u201ca bundle of coefficients.\u201d ([3], pg. 190) In this case, with \u201c<em>E <\/em>X<em> I<\/em>\u201c, <em>I<\/em> is an isotopy, and the zero space is the tangent space. There is \u201cno left distributive law\u201d ([3], pg. 122), because orbital electrons absorb gravitons at various rates.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Hein, Morris, \u201cFoundations of College Chemistry, Fourth Edition\u201d, DICKENSON PUBLISHING COMPANY, INC., c. 1977<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2] Whitney, Hassler, \u201cDifferential Manifolds\u201d, The Annals of Mathematics, Second Series, Vol. 37. No. 3 (Jul., 1936) pp. 645-680<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3] Steenrod, Norman, \u201cThe Topolgy of Fibre Bundles\u201d, Princeton University Press, c. 1951<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In Chemistry, \u201cThis phenomenon of two or more compounds having the same molecular formula but different structures is called isomerism.\u201d ([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 \u201can m-dimensionable manifold M of class [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,10,16],"tags":[],"class_list":["post-1093","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-nuclear-physics","category-quantum-field-theory"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1093","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/comments?post=1093"}],"version-history":[{"count":1,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1093\/revisions"}],"predecessor-version":[{"id":1094,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1093\/revisions\/1094"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=1093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=1093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=1093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}