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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cohomology of the symplectic group $\textrm {Sp}_ 4(\textbf {Z})$. I. The odd torsion case
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by Alan Brownstein and Ronnie Lee PDF
Trans. Amer. Math. Soc. 334 (1992), 575-596 Request permission

Abstract:

Let ${h_2}$ be the degree two Siegel space and $Sp(4,\mathbb {Z})$ the symplectic group. The quotient $Sp(4,\mathbb {Z})\backslash {h_2}$ can be interpreted as the moduli space of stable Riemann surfaces of genus $2$. This moduli space can be decomposed into two pieces corresponding to the moduli of degenerate and nondegenerate surfaces of genus $2$. The decomposition leads to a Mayer-Vietoris sequence in cohomology relating the cohomology of $Sp(4,\mathbb {Z})$ to the cohomology of the genus two mapping class group $\Gamma _2^0$. Using this tool, the $3$- and $5$-primary pieces of the integral cohomology of $Sp(4,\mathbb {Z})$ are computed.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 334 (1992), 575-596
  • MSC: Primary 11F75; Secondary 11F46, 32G15
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1055567-X
  • MathSciNet review: 1055567