An effective estimate on Betti numbers
Lei Ni
TL;DR
This paper presents a new effective method to estimate Betti numbers of the loop space of certain compact manifolds, extending previous polynomial estimates by considering the limit of infinite Grauert tube radius.
Contribution
It introduces an effective estimate on Betti numbers for manifolds with finite Grauert tubes, advancing the understanding of their topological complexity.
Findings
Provides an explicit estimate on Betti numbers
Extends polynomial estimates to infinite tube radius limit
Enhances understanding of loop space topology
Abstract
We provide an effective estimate on the Betti numbers of the loop space of a compact manifold which admits a finite Grauert tube. It implies the polynomial estimate in \cite{Chen} after taking the radius of the tube to infinity.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows