Abstract
Let L be a lattice in a real vector space W. Then the quotient W/L is a real torus. Using a basis l1,..., l2 of L we have an isomorphism \( \varphi :{(\mathbb{R}/\mathbb{Z})^{n}} = \mathbb{R}/{\mathbb{Z}^{n}}\mathop{ \to }\limits^{ \approx } W/L \) which sends a real n-vector (λ1,..., λ n ) to the L-coset ∑λ j l j . Thus a real torus is topologically isomorphic to a product of circles. Consequently the algebraic topology of V/L is obvious.
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© 1991 Springer-Verlag Berlin Heidelberg
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Kempf, G.R. (1991). The Cohomology of Complex Tori. In: Complex Abelian Varieties and Theta Functions. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76079-2_3
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DOI: https://doi.org/10.1007/978-3-642-76079-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53168-5
Online ISBN: 978-3-642-76079-2
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