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- W1526074704 abstract "Let $Y$ be a compact, oriented 3-manifold with a contact form $a$ and a metric $ds^2$. Suppose that $Fto Y$ is a principal bundle with structure group $U(2) = SU(2)times_{pm1}S^1$ such that $F/S^1$ is the principal SO(3) bundle of orthonormal frames for $TY$. A unitary connection $A_0$ on the Hermitian line bundle $Ftimes_{det U(2)}mathbb{C}$ determines a self-adjoint Dirac operator $D_0$ on the $mathbb{C}^2$-bundle $Ftimes_{U(2)}mathbb{C}^2$. The contact form $a$ can be used to perturb the connection $A_0$ by $A_0-ira$. This associates a one parameter family of Dirac operators $D_r$ for $rgeq0$. When $r>>1$, we establish a sharp sup-norm estimate on the eigensections of $D_r$ with small eigenvalues. The sup-norm estimate can be applied to study the asymptotic behavior of the spectral flow from $D_0$ to $D_r$. In particular, it implies that the subleading order term of the spectral flow is strictly smaller than the order of $r^{frac{3}{2}}$. We also relate the $eta$-invariant of $D_r$ to certain spectral asymmetry function involving only the small eigenvalues of $D_r$." @default.
- W1526074704 created "2016-06-24" @default.
- W1526074704 creator A5032302661 @default.
- W1526074704 date "2013-07-17" @default.
- W1526074704 modified "2023-09-27" @default.
- W1526074704 title "Dirac spectral flow on contact three manifolds I: eigensection estimates and spectral asymmetry" @default.
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