𝕋²–cobordism of quasitoric 4–manifolds

Abstract

T 2-cobordism of quasitoric 4-manifolds SOUMEN SARKAR We show the T 2-cobordism group of the category of 4-dimensional quasitoric manifolds is generated by the T 2-cobordism classes of CP 2. We construct nice oriented T 2 manifolds with boundary whose boundaries are the Hirzebruch surfaces. The main tool is the theory of quasitoric manifolds. 55N22; 57R90

A new construction of lens spaces

“…In this section we construct oriented T n -manifold with boundary where the boundary is a disjoint union of lens spaces. Similar construction can be found in Section 4 of [Sar12]. Let Q be an n-dimensional simple convex polytope in R n with facets F 1 , .…”

Orientability and equivariant oriented cobordism of 2-torus manifolds

“…We remark that similar construction of manifolds with corners arises in [Sar12,SS13a,Sar15,SS16]. When η is trivial we denote the space W (Y, λ, η) by W (Y, λ).…”

“…Definition 3.1 generalizes the notion of vertex cut of edge simple polytopes, which was introduced in Section 2 of [Sar12] to study equivariant cobordism quasitoric manifolds. The concept of face-simple polytpe also appears in [Sar15] and [SS16].…”

Equilibrium triangulations of some quasitoric 4-manifolds

“…Equivariant connected sum of quasitoric manifolds is discussed in 1.11 of [DJ91] as well as in Section 2 of [Sar12]. The following Proposition classifies all 4-dimensional quasitoric manifolds.…”