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Re: Vozrazenia Goshi
Secheniya rassloenii ne klassificiruyutsya gomologiyami bazy s koefficientami v gomotopiyah sloya. V sluchae $S^n, n>2$ v $H^n(S^n,\pi_{n-1}(F))$ lezhit prepyatstvie k suschestvovaniyu secheniya. V obschem sluchae vse slozhnee, tak kak prepyatstvii celaya seriya.
Voobsche, dlya togo chtoby znat' gomotopicheskuyu klassifikaciyu sechenii, nedostatochno znat' gomotopicheskie tipy bazy i sloya. Naprimer, u trivial'nogo rassloeniya $S^4\times S^3\to S^4$ est' secheniya, a u kvaternionnogo rassloeniya Hopfa $S^3\subset S^7\to S^4$ -- net (eto glavnoe SU(2)-rassloenie, i esli by u nego byli secheniya, ono bylo by trivial'nym).
Chto-to v takom duhe.
Secheniya rassloenii ne klassificiruyutsya gomologiyami bazy s koefficientami v gomotopiyah sloya. V sluchae $S^n, n>2$ v $H^n(S^n,\pi_{n-1}(F))$ lezhit prepyatstvie k suschestvovaniyu secheniya. V obschem sluchae vse slozhnee, tak kak prepyatstvii celaya seriya.
Voobsche, dlya togo chtoby znat' gomotopicheskuyu klassifikaciyu sechenii, nedostatochno znat' gomotopicheskie tipy bazy i sloya. Naprimer, u trivial'nogo rassloeniya $S^4\times S^3\to S^4$ est' secheniya, a u kvaternionnogo rassloeniya Hopfa $S^3\subset S^7\to S^4$ -- net (eto glavnoe SU(2)-rassloenie, i esli by u nego byli secheniya, ono bylo by trivial'nym).
Chto-to v takom duhe.
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