TY - JOUR

T1 - String structures associated to indefinite Lie groups

AU - Sati, Hisham

AU - Shim, Hyung bo

N1 - Funding Information:
We would like to thank Domenico Fiorenza, Corbett Redden, Jonathan Rosenberg, and Urs Schreiber for very useful discussions. The research of H. S. was supported by the National Science Foundaton NSF, USA Grant PHY-1102218 . We are grateful to the anonymous referee for very useful suggestions that have substantially improved the paper.

PY - 2019/6

Y1 - 2019/6

N2 - String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signature orthogonal group O(n) to the indefinite-signature orthogonal group O(p,q), i.e. from the Riemannian to the pseudo-Riemannian setting. This requires that we work at the unstable level, which makes the discussion more subtle than the stable case. Similar, but much simpler, constructions hold for other noncompact Lie groups such as the unitary group U(p,q) and the symplectic group Sp(p,q). This extension provides a starting point for an abundance of constructions in (higher) geometry and applications in physics.

AB - String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signature orthogonal group O(n) to the indefinite-signature orthogonal group O(p,q), i.e. from the Riemannian to the pseudo-Riemannian setting. This requires that we work at the unstable level, which makes the discussion more subtle than the stable case. Similar, but much simpler, constructions hold for other noncompact Lie groups such as the unitary group U(p,q) and the symplectic group Sp(p,q). This extension provides a starting point for an abundance of constructions in (higher) geometry and applications in physics.

KW - Classifying spaces

KW - Indefine Lie groups

KW - Pontrjagin classes

KW - Pseudo-orthogonal group

KW - String structures

KW - Whitehead tower

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U2 - 10.1016/j.geomphys.2019.02.002

DO - 10.1016/j.geomphys.2019.02.002

M3 - Article

AN - SCOPUS:85062959785

VL - 140

SP - 246

EP - 264

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -