The moduli of flat PU(2,1) structures on Riemann surfaces

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28 引文 斯高帕斯(Scopus)

摘要

For a compact Riemann surface X of genus g > 1, Hom(π1(X), PU(p, q))/PU(p, q) is the moduli space of flat PU(p, q)-connections on X. There are two integer invariants, dP, dQ, associated with each σ ∈ Hom(π1(X), PU(p, q))/PU(p, q). These invariants are related to the Toledo invariant τ by τ = 2qdP-pdQ/p+q. This paper shows, via the theory of Higgs bundles, that if q = 1, then -2(g - 1) ≤ τ ≤ 2(g - 1). Moreover, Hom(π1(X), PU(2, 1))/PU(2, 1) has one connected component corresponding to each τ ∈ 2/3ℤ with -2(g - 1) ≤ τ ≤ 2(g - 1). Therefore the total number of connected components is 6(g - 1) + 1.

原文English
頁(從 - 到)231-256
頁數26
期刊Pacific Journal of Mathematics
195
發行號1
DOIs
出版狀態Published - 2000 9月

All Science Journal Classification (ASJC) codes

  • 一般數學

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