Remarks on Framed Bordism Classes of Classical Lie Groups

Minami, Haruo

doi:10.2977/prims/1201011791

Cited by 1 publication

(3 citation statements)

References 10 publications

(18 reference statements)

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“…For 1 ≤ q ≤ n − 1, let V n,q denote the Stiefel manifold of orthogonal q-frames in F n , where F = R, C, H. Then, from [50], the element [V n,q , φ] = 0 for a framing φ in the sense of [45]. [51]: For any two real representations ρ 1 and ρ 2 of G, and for the adjoint representation Ad G , the following holds [G,…”

Section: Framed Cobordismmentioning

confidence: 99%

“…So the framed manifold (Z, φ) bounds the framed manifold (G, −f ). See [51] for more details. More examples can be found in [4].…”

Section: Framed Boundariesmentioning

confidence: 99%

“…2. Effect of change of orientation [9]: Changing the orientation results in a possible reversal of sign of the corresponding class [51]: For any two real representations ρ 1 and ρ 2 of G, and for the adjoint representation Ad G , the following holds [G, Ad G −ρ…”

Section: Framed Cobordismmentioning

confidence: 99%

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M-Theory with Framed Corners and Tertiary Index Invariants

Sati¹

2014

SIGMA

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Abstract. The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f -invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a physical realization and interpretation of some ingredients appearing in the constructions due to Bunke-Naumann and Bodecker. The formulation leads to a natural interpretation of anomalies using corners and uncovers some resulting constraints in the heterotic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function.

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Section: Framed Cobordismmentioning

confidence: 99%

“…So the framed manifold (Z, φ) bounds the framed manifold (G, −f ). See [51] for more details. More examples can be found in [4].…”

Section: Framed Boundariesmentioning

confidence: 99%