TY - JOUR
T1 - Elementary orbifold differential topology
AU - Borzellino, Joseph E.
AU - Brunsden, Victor
PY - 2012/11/1
Y1 - 2012/11/1
N2 - Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts.
AB - Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts.
UR - http://www.scopus.com/inward/record.url?scp=84866944349&partnerID=8YFLogxK
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U2 - 10.1016/j.topol.2012.08.032
DO - 10.1016/j.topol.2012.08.032
M3 - Article
AN - SCOPUS:84866944349
SN - 0166-8641
VL - 159
SP - 3583
EP - 3589
JO - Topology and its Applications
JF - Topology and its Applications
IS - 17
ER -