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The fundamental group of locally standard $T$–manifolds

Haozhi Zeng

Algebraic & Geometric Topology 18 (2018) 3031–3035

We calculate the fundamental group of locally standard T–manifolds under the assumption that the principal T–bundle obtained from the free T–orbits is trivial. This family of manifolds contains nonsingular toric varieties which may be noncompact, quasitoric manifolds and toric origami manifolds with coörientable folding hypersurface. Although the fundamental groups of the above three kinds of manifolds are well-studied, we give a uniform and simple method to generalize the formulas of their fundamental groups.

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fundamental group, torus manifolds
Mathematical Subject Classification 2010
Primary: 14F35, 57S25
Secondary: 57R19
Received: 27 September 2017
Revised: 15 February 2018
Accepted: 29 April 2018
Published: 22 August 2018
Haozhi Zeng
School of Mathematical Sciences
Fudan University