Topology at the Planck length

Madore, J.; Saeger, L.A.

doi:10.1088/0264-9381/15/4/009

Topology at the Planck length

J. Madore
(
- Orsay
)
,
L.A. Saeger
(
- Orsay
)

May, 1997

17 pages

Published in:

Class.Quant.Grav. 15 (1998) 811-826

e-Print:

gr-qc/9708053 [gr-qc]

DOI:

10.1088/0264-9381/15/4/009

Report number:

LPTHE-ORSAY-97-34

View in:

pdf

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Abstract: (arXiv)

A basic arbitrariness in the determination of the topology of a manifold at the Planck length is discussed. An explicit example is given of a `smooth' change in topology from the 2-sphere to the 2-torus through a sequence of noncommuting geometries. Applications are considered to the theory of D-branes within the context of the proposed

M

(atrix) theory.

fundamental constant: length
space-time: sphere
space-time: torus
dimension: 2
topology
differential geometry: noncommutative
differential forms
Riemann surface
membrane model: D-brane
field theory: M-theory

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