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.
Publisher Copyright:
© 2019 Elsevier B.V.
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
SN - 0393-0440
VL - 140
SP - 246
EP - 264
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -