Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 5 (2015), 2707-2754.
Pontryagin classes of locally symmetric manifolds
Pontryagin classes are basic invariants of a smooth manifold , and many topological problems can be reduced to computing these classes. For a locally symmetric manifold, Borel and Hirzebruch gave an algorithm to determine if is nonzero. In addition they implemented their algorithm for a few well-known and for , . Nevertheless, there remained several for which their algorithm was not implemented. In this note we compute low-degree Pontryagin classes for every closed, locally symmetric manifold of noncompact type. As a result of this computation, we answer the question: Which closed locally symmetric have at least one nonzero Pontryagin class?
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2707-2754.
Received: 9 April 2014
Revised: 14 December 2014
Accepted: 10 January 2015
First available in Project Euclid: 16 November 2017
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Tshishiku, Bena. Pontryagin classes of locally symmetric manifolds. Algebr. Geom. Topol. 15 (2015), no. 5, 2707--2754. doi:10.2140/agt.2015.15.2709. https://projecteuclid.org/euclid.agt/1510841029