| GÖKOVA GEOMETRY / TOPOLOGY PROCEEDINGS |
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| Published in |
Proceedings of Gökova Geometry-Topology Conference 2014 |
| Title |
The space of paths in complex projective space with real boundary conditions |
| Authors |
Nancy Hingston and Alexandru Oancea |
| Abstract |
We compute the homology of the space of paths in ℂPn with endpoints in ℝPn, n ≥ 1 and its algebra structure with respect to the Pontryagin-Chas-Sullivan product with ℤ/2-coefficients. In the orientable case (n odd) we also compute its integral homology. Our method combines Morse theory with geometry and yields and explicit description of cycles representing all homology classes. |
| Keywords |
Path space, loop space, projective space, Fubini-Study metric, Pontryagin product, Chas-Sullivan product, Morse theory, perfect Morse-Bott function, completing manifold
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| Pages | 192-233 |
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