The Κ Ring of the Moduli of Curves of Compact Type: I

The Κ Ring of the Moduli of Curves of Compact Type: Ii

The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ classes is studied. Relations, constructed via the virtual geometry of the moduli of stable maps, are used to prove universality results relating the κ rings in genus 0 to higher genus. Predictions for κ classes of the Gorenstein conjecture are proven.

Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations

In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

Compactification of κ-Frames

$z^circ$-filters and related ideals in $C(X)$

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

Recursion Formulae of Higher Weil-petersson Volumes

Abstract. In this paper we study effective recursion formulae for computing intersection numbers of mixed ψ and κ classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani’s recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the...