اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Hopf Index Theorem for foliations
375
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf closures. The primary tool used to establish this result is an adaptation to foliations of the Witten deformation method.
قيم البحث
اقرأ أيضاً
In this paper, we study stability for harmonic foliations on locally conformal Kahler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces.
The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators ca
n be given natural interpretations using this language and that the resulting formula is still an identity.
We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use this index t
o define the relative $eta$-invariant $eta(A_1,A_0)$ of two strongly Callias-type operators, which are equal outside of a compact set. Even though in our situation the $eta$-invariants of $A_1$ and $A_0$ are not defined, the relative $eta$-invariant behaves as if it were the difference $eta(A_1)-eta(A_0)$. We also define the spectral flow of a family of such operators and use it compute the variation of the relative $eta$-invariant.
We present a new systematic approach to constructing spherical codes in dimensions $2^k$, based on Hopf foliations. Using the fact that a sphere $S^{2n-1}$ is foliated by manifolds $S_{coseta}^{n-1} times S_{sineta}^{n-1}$, $etain[0,pi/2]$, we distri
bute points in dimension $2^k$ via a recursive algorithm from a basic construction in $mathbb{R}^4$. Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between achieving a large number of codewords for a minimum given distance and effective constructiveness with low encoding computational cost. Bounds for the asymptotic density are derived and compared with other constructions. The encoding process has storage complexity $O(n)$ and time complexity $O(n log n)$. We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity $O(n log n)$.
Let $Gamma$ be a finitely generated discrete group satisfying the rapid decay condition. We give a new proof of the higher Atiyah-Patodi-Singer theorem on a Galois $Gamma$-coverings, thus providing an explicit formula for the higher index associated
to a group cocycle $cin Z^k (Gamma;mathbb{C})$ which is of polynomial growth with respect to a word-metric. Our new proof employs relative K-theory and relative cyclic cohomology in an essential way.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
