Department of Mathematical Sciences
Camden, NJ 08102
- Differential Topology, Riemannian Geometry
- Higher Â-genera on certain non-spin S¹-manifolds, Topology and its Applications 157 (2010), no. 9, 1658-1663.
- Complex contact manifolds and S1 actions. Geom. Dedicata 149 (2010), 335–345.
- Rigidity and vanishing theorems for almost quaternionic manifolds. Geom. Dedicata 134 (2008),139–152.
- Positively curved π2-finite manifolds, C.R. Math. Acad. Sci. Paris. 345 (2007), no. 9, 499–502.
- Spin-q manifolds and S¹ actions, with R. Herrera, C. R. Acad. Sci. Paris, Ser. I 345 (2007) 35–38.
- Spin-q manifolds admitting parallel and Killing spinors, with R. Herrera, J. Geom. Phys. 57 (2007), no. 7, 1525—1539.
- The signature of even 4-manifolds with circle actions, J JP J. Geom. Topol. 6 (2006), no. 3, 237–243.
- Elliptic genera for non-spin Riemannian symmetric spaces with b2=0, with R. Herrera, Journal of Geometry and Physics 49 (2004), no. 2, 197–205.
- The signature and the elliptic genus of π2-finite manifolds with circle actions, with R. Herrera, Topology and its Applications 136 (2004) 251-259.
- Erratum to “The signature and the elliptic genus of π2-finite manifolds with circle actions” [Topology Appl. 136 (1-3) (2004) 251–259]. Topology Appl. 157 (2010), no. 13, 2157
- Generalized elliptic genus and cobordism class of non-spin real Grassmannians, with R. Herrera, Annals of Global Analysis and Geometry 24 (2003) 323-335.
- A result on the Â and elliptic genera on non-spin manifolds with circle actions, with R. Herrera, Comptes Rendus de l’Académie des Sciences – Série I – Mathematics 335 (2002), no. 4, 371-374.
- Classification of positive quaternion-Kaehler 12-manifolds, with R. Herrera, Comptes Rendus de l’Académie des Sciences – Série I – Mathematics 334 (2002), no. 1, 43-46.
- Â-genus on non-spin manifolds with circle actions and the classification of positive quaternion-Kähler 12-manifolds, with R. Herrera, Journal of Differential Geometry 61 (2002)., no. 3, 341-364.
- Erratum to “Â -genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds” . J. Differential Geometry 90 (2012), no. 3, 521.
- Gromov Invariants of S²-bundles over 4-manifolds, Topology and its Applications, vol. 124 (2002), no.2, 327-345.
- Geometrical Themes Inspired by the N-body Problem. Springer Verlag (2018).
Works in Progress
- Examples of Hamiltonian circle actions and π1 of the space of Hamiltonian symplectomorphisms of manifolds of dimension 6, preprint (2016).
- Modular invariance and almost even-Clifford Hermitian Manifolds, preprint (2023).
- Undergraduate level:
Calculus I, II, III, Advanced Calculus, Linear Algebra, Discrete Mathematics, Advanced Linear Algebra, Advanced Calculus, Introduction to Topology, Geometry, Introduction to Differential Geometry.
- Graduate level:
Linear Algebra and its Applications, Abstract Algebra, Geometry, Differential Geometry, Topology.