Geodesic
Pontryagin classes of locally symmetric manifolds
Tshishiku, Bena1
1Department of Mathematics, University of Chicago, Chicago, IL 60615, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2707-2754
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Pontryagin classes pi(M) are basic invariants of a smooth manifold M, 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 pi(M) is nonzero. In addition they implemented their algorithm for a few well-known M and for i = 1, 2. Nevertheless, there remained several M 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 M have at least one nonzero Pontryagin class?

DOI : 10.2140/agt.2015.15.2709
Keywords: algebraic topology, differential geometry, characteristic classes

Tshishiku, Bena  1

1 Department of Mathematics, University of Chicago, Chicago, IL 60615, USA 
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Tshishiku, Bena. Pontryagin classes of locally symmetric manifolds. Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2707-2754. doi: 10.2140/agt.2015.15.2709

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