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Topologia Algebrica: Fascio, Omologia, Gruppo Fondamentale, Mapping Class Group, Teorema Di Van Kampen, Omotopia, Rivestimento, 55-XX

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Topologia Algebrica: Fascio, Omologia, Gruppo Fondamentale, Mapping Class Group, Teorema Di Van Kampen, Omotopia, Rivestimento, 55-XX

Penned By Fonte Wikipedia
4.85 63,376 Ratings
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Editor's Note:
Fonte: Wikipedia. Pagine: 39. Capitoli: Fascio, Omologia, Gruppo fondamentale, Mapping class group, Teorema di Van Kampen, Omotopia, Rivestimento, 55-XX, Spazio semplicemente connesso, Gruppi di omotopia, Grado topologico, Complesso di celle, Caratteristica di Eulero, Gruppo topologico, Omologia singolare, Formula di Eulero per i poliedri, Genere, Fibrato, Indice di avvolgimento, Sollevamento, Successione di Mayer-Vietoris, Germe di funzione, Coomologia di De Rham, Algebra omologica, Complesso di catene, Teorema del sollevamento dell'omotopia, Teorema di unicita del sollevamento, Fibrato vettoriale, Teorema di Borsuk, Numero di Betti, Nerbo. Estratto: In matematica, un fascio e uno degli strumenti fondamentali per lo studio delle proprieta geometriche degli oggetti. Un fascio permette di esprimere le relazioni tra piccole regioni di uno spazio topologico e lo spazio totale. Per costruire un fascio si parte, in genere, da uno spazio topologico X, e si assegna ad ogni sottoinsieme aperto U di X un dato F(U), quale un insieme, un gruppo, o un anello. In genere, se si vogliono studiare proprieta geometriche dello spazio topologico X, il dato F(U) assegnato all'aperto U e costituito da una famiglia di oggetti geometrici definiti su U, come funzioni, campi vettoriali, o forme differenziali. Il primo passo per poter definire un fascio e definire il concetto di prefascio, con il quale si formalizza l'idea di associare determinati dati ad ogni aperto. In seguito, si enunciano i due assiomi di fascio: la normalizzazione e l'incollamento. Sia X uno spazio topologico, e sia C una categoria. In genere, C puo essere la categoria degli insiemi, dei gruppi, dei gruppi abeliani, o quella degli anelli commutativi. Un prefascio F su X a valori in C e allora definito dai dati seguenti: I morfismi resV, U sono detti morfismi di restrizione, e devono soddisfare le due proprieta seguenti: Il secondo assioma afferma che il risultato della restrizione prima da U a V ed in seguito da V a ..

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"I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average."
Anthony Nguyen
Anthony Nguyen December 20, 2024
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Margaret Nguyen
Margaret Nguyen September 03, 2024
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Elizabeth  Davis
Elizabeth Davis March 20, 2024
"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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