Mathematics – Geometric Topology
Scientific paper
2010-01-06
Geom Dedicata (2011) 152:197-211
Mathematics
Geometric Topology
18 p; final version
Scientific paper
10.1007/s10711-010-9553-0
To the integral symplectic group Sp(2g,Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the Siegel space of genus g has the homotopy type of a bouquet of (g-2)-spheres. This, in turn, implies that the rational homology of moduli space of (unmarked) principal polarized abelian varieties of genus g modulo the decomposable ones vanishes in degree g-2 or lower. Another application is an improved stability range for the homology of the symplectic groups over Euclidean rings. But the original motivation comes from envisaged applications to the homology of groups of Torelli type. The proof of our main result rests on a refined nerve theorem for posets that may have an interest in its own right.
der Kallen Wilberd van
Looijenga Eduard
No associations
LandOfFree
Spherical complexes attached to symplectic lattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spherical complexes attached to symplectic lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spherical complexes attached to symplectic lattices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-164222