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Barycentric straightening and bounded co...
Lafont, Jean-Franço...

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Barycentric straightening and bounded cohomology by Lafont, Jean-François ( Author )
Lemonjar Open Access
N.A
22-03-2015
We study the barycentric straightening of simplices in irreducible symmetric spaces of non-compact type. We show that, for an n-dimensional symmetric space of rank r>1, the p-Jacobian has uniformly bounded norm, as soon as p is at least n-r+2. As a consequence, for a non-compact, connected, semisimple real Lie group G, in degrees n-r+2 and higher, every cohomology class has a bounded representative. This answers Dupont's problem in small codimension. We also give examples of symmetric spaces where the barycentrically straightened simplices of dimension n-r have unbounded volume, showing that the range in which we obtain boundedness of the p-Jacobian is very close to optimal.
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English
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MYR 0.01
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https://arxiv.org/abs/1503.06369
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