On an algebraic formula and applications to group action on manifolds

We consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound of the number of fixed points. We also give an obstruction to the existence of $\mathbb{Z}_p$ action on manifolds with isolated fixed points when $p$ is a prime.Comment: 7 pages, revised slightly to update a new reference and reassign the credit of the idea in this not

Some remarks on circle action on manifolds

This paper contains several results concerning circle action on almost-complex and smooth manifolds. More precisely, we show that, for an almost-complex manifold $M^{2mn}$(resp. a smooth manifold $N^{4mn}$), if there exists a partition $\lambda=(\lambda_{1},...,\lambda_{u})$ of weight $m$ such that the Chern number $(c_{\lambda_{1}}... c_{\lambda_{u}})^{n}[M]$ (resp. Pontrjagin number $(p_{\lambda_{1}}... p_{\lambda_{u}})^{n}[N]$) is nonzero, then \emph{any} circle action on $M^{2mn}$ (resp. $N^{4mn}$) has at least $n+1$ fixed points. When an even-dimensional smooth manifold $N^{2n}$ admits a semi-free action with isolated fixed points, we show that $N^{2n}$ bounds, which generalizes a well-known fact in the free case. We also provide a topological obstruction, in terms of the first Chern class, to the existence of semi-free circle action with \emph{nonempty} isolated fixed points on almost-complex manifolds. The main ingredients of our proofs are Bott's residue formula and rigidity theorem.Comment: 10 pages,to appear in Mathematical Research Letter

Circle action and some vanishing results on manifolds

Kawakubo and Uchida showed that, if a closed oriented $4k$-dimensional manifold $M$ admits a semi-free circle action such that the dimension of the fixed point set is less than $2k$, then the signature of $M$ vanishes. In this note, by using $G$-signature theorem and the rigidity of the signature operator, we generalize this result to more general circle actions. Combining the same idea with the remarkable Witten-Taubes-Bott rigidity theorem, we explore more vanishing results on spin manifolds admitting such circle actions. Our results are closely related to some earlier results of Conner-Floyd, Landweber-Stong and Hirzebruch-Slodowy.Comment: 7 pages, typos corrected and minors modifie

Biometric Person Identification Using Near-infrared Hand-dorsa Vein Images

Biometric recognition is becoming more and more important with the increasing demand for security, and more usable with the improvement of computer vision as well as pattern recognition technologies. Hand vein patterns have been recognised as a good biometric measure for personal identification due to many excellent characteristics, such as uniqueness and stability, as well as difficulty to copy or forge. This thesis covers all the research and development aspects of a biometric person identification system based on near-infrared hand-dorsa vein images. Firstly, the design and realisation of an optimised vein image capture device is presented. In order to maximise the quality of the captured images with relatively low cost, the infrared illumination and imaging theory are discussed. Then a database containing 2040 images from 102 individuals, which were captured by this device, is introduced. Secondly, image analysis and the customised image pre-processing methods are discussed. The consistency of the database images is evaluated using mean squared error (MSE) and peak signal-to-noise ratio (PSNR). Geometrical pre-processing, including shearing correction and region of interest (ROI) extraction, is introduced to improve image consistency. Image noise is evaluated using total variance (TV) values. Grey-level pre-processing, including grey-level normalisation, filtering and adaptive histogram equalisation are applied to enhance vein patterns. Thirdly, a gradient-based image segmentation algorithm is compared with popular algorithms in references like Niblack and Threshold Image algorithm to demonstrate its effectiveness in vein pattern extraction. Post-processing methods including morphological filtering and thinning are also presented. Fourthly, feature extraction and recognition methods are investigated, with several new approaches based on keypoints and local binary patterns (LBP) proposed. Through comprehensive comparison with other approaches based on structure and texture features as well as performance evaluation using the database created with 2040 images, the proposed approach based on multi-scale partition LBP is shown to provide the best recognition performance with an identification rate of nearly 99%. Finally, the whole hand-dorsa vein identification system is presented with a user interface for administration of user information and for person identification