Oriented Cobordism of $\CP^{2k+1}$

TL;DR

This paper introduces a novel method to construct oriented manifolds with boundaries equivalent to complex projective spaces of odd dimension, utilizing quasitoric manifolds to advance the understanding of cobordism classes.

Contribution

It provides a new construction technique for oriented manifolds with boundaries of complex projective spaces using quasitoric manifolds, expanding cobordism theory.

Findings

Constructed oriented manifolds with boundary $ ext{CP}^{2k+1}$ for all $k \\geq 0$

Applied quasitoric manifolds as a key tool in cobordism construction

Enhanced understanding of the cobordism class of complex projective spaces

Abstract

We give a new construction of oriented manifolds having the boundary $\CC P^{2k+1}$ for each $k \geq 0$. The main tool is the theory of quasitoric manifolds.