Manuscript I-B-VP-1@1 · I-B-VP-1-v1.tex · section · 6d700be9

Geometry and the additional smooth structure

The completion, regular data, and Ward prescription › Geometry and the additional smooth structure · lines 209–230

Fix

0 < α < 1, μ = 2 π (1 - α), 0 \leq β < 1, ξ \in R .

The regular host is

M = R_{t} \times (0, \infty)_{r} \times (R /2 π Z)_{φ} \times R_{z},

g = - d t^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2} .

Its metric completion adds

W = R_{t} \times {o} \times R_{z},

a worldsheet, not a worldline CheungIB,CheungIBG.

Displayed formulas in this passage

unlabeled · line 212
$0 < α < 1, μ = 2 π (1 - α), 0 \leq β < 1, ξ \in R .$
unlabeled · line 218
$M = R_{t} \times (0, \infty)_{r} \times (R /2 π Z)_{φ} \times R_{z},$
unlabeled · line 222
$g = - d t^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2} .$
unlabeled · line 226
$W = R_{t} \times {o} \times R_{z},$