Announcement of a Projective Theory of Affinely Connected by Thomas T. Y.

By Thomas T. Y.

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That ∞ = D d∗ (d| D(∆) ∩ δCabs δC ∞ ) . abs 2 = {x ∈ H 2 ; i∗ (∗x) = 0 = i∗ (∗dx)} ⊂ D(d∗ d). Now D(∆) = Habs 1 ∩ δC ∞ and dx ∈ H 1 . e. (d + δ)x ∈ H 1 because δx = 0. Since also i∗ (∗x) = 0, by elliptic regularity x ∈ H 2 . The boundary conditions are fulfilled therefore x ∈ 2 = D(∆). Habs The proof for (dδ)|dC ∞ is similar. 17. Let N be a compact Riemannian manifold possibly with boundary. Then √ ∗ ∗ F ∆⊥ p [N ], λ = Fp Lp [N ], λ + Fp−1 Lp [N ], λ . Proof. 4 by the following calculation: √ √ √ p+1 p d | ∞ p+1 , λ)+F (dp−1 δ p | ∞ p−1 , λ) F ∆⊥ p [N ], λ = F (δ δCabs (Λ = F (d | p ∞ (Λp+1 (N )) δCabs (N )) dC0 (Λ p−1 , λ) + F (d | ∞ (Λp−1 (N)) δCabs (N)) , λ) = Fp L∗p [N ], λ + Fp−1 L∗p−1 [N ], λ .

Mech. Anal. 41 (1971), 163–218. [GroSh] M. A. Shubin, Von Neumann spectra near zero, GAFA 1 (1991), 375–404. [HS] E. Hess, T. Schick, Nonvanishing of L2 -torsion of hyperbolic manifolds, Manuscripta Mathematica 97 (1998), 329–334. [L] J. Lott, Heat kernels on covering spaces and topological invariants, Journal of Differential Geometry 35 (1992), 471–510. ¨ck, L2 -topological invariants of 3-manifolds, Inven[LL¨ u] J. Lott, W. Lu tiones Math. 120 (1995), 15–60. ¨ ck, Analytic and topological torsion for manifolds with boundary [L¨ u1] W.

W. LUCK AND T. SCHICK 562 GAFA Branson/Gilkey [BrG] explicitly compute the first few coefficients of the asymptotic expansion of the heat operator for manifolds with boundary and local boundary conditions. We will use these results to give two and three dimensional examples with nontrivial metric anomaly. Using a product formula this yields examples also in arbitrary dimensions > 1. The examples Dimension = 2. Here, we work with S 1 × [0, 3]. On S 1 × [0, 1), we choose the following family of metrics: gu = f (x, u)(dx2 + dy 2 ) with (y, x) ∈ S 1 × [0, 1) .

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