Read e-book online Darwin: A Very Short Introduction (Very Short Introductions) PDF

By Jonathan Howard

ISBN-10: 0192854542

ISBN-13: 9780192854544

Darwin's conception that man's ancestors have been apes prompted an uproar in the clinical global, in addition to public frenzy while The foundation of Species used to be released in 1859.

Arguments nonetheless rage concerning the implications of his evolutionary concept, and skepticism in regards to the price of Darwin's contribution to wisdom is frequent. during this research of Darwin's significant insights and arguments, Jonathan Howard reasserts the significance of Darwin's paintings for the advance of recent biology. He deals a stimulating view of the well-known scientist in a concise, convenient layout, making it a masterpiece for all Darwinians in addition to for all normal readers of well known technological know-how.

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Extra resources for Darwin: A Very Short Introduction (Very Short Introductions)

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21. Комплексные векторные расслоения GL(n, C)-изоморфны тогда и только тогда, когда они U (n)-изоморфны. Доказательство.

U2 . е. что сфера S 3 гомеоморфна произведению 2 S × S 1 . 4, π1 (S 2 × S 1 ) = π1 (S 2 ) π1 (S 1 ) = Z. Б. Антоневич получаем противоречие. Таким образом, построенное расслоение сферы S 3 на окружности нетривиально. Заметим, что тривиализации достаточно построить над меньшими множествами U1 = {z ∈ C : |z| ≤ 1}, U2 = {z ∈ C : z ≥ 1}, (17) так как они тоже образуют покрытие. Упражнение. Сферу S 3 можно реализовать как R3 , к которому присоединена точка ∞. Построить расслоение Хопфа для такой реализации S 3 .

K (S n ) = 0 при k < n. Схема доказательства. Сфероид ϕ : I k → S n можно приблизить гладким отображением, которое гомотопно исходному. При k < n образ гладкого сфероида не может иметь размерность, большую k, поэтому образ гладкого сфероида не совпадает со всей сферой S n . Пусть x0 ∈ S n и эта точка не принадлежит образу сфероида. Пространство S n \ x0 гомеоморфно шару, является стягиваемым пространством, поэтому сфероид гомотопен постоянному отображению. Первый результат о нетривиальности гомотопических групп сферы S n при n ≥ 2 в был получен Хопфом (H.

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Darwin: A Very Short Introduction (Very Short Introductions) by Jonathan Howard

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