A class of torus manifolds with nonconvex orbit space
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- by Mainak Poddar and Soumen Sarkar PDF
- Proc. Amer. Math. Soc. 143 (2015), 1797-1811 Request permission
Abstract:
We study a class of smooth torus manifolds whose orbit space has the combinatorial structure of a simple polytope with holes. We construct moment angle manifolds for such polytopes with holes and use them to prove that the associated torus manifolds admit stable almost complex structure. We give a combinatorial formula for the Hirzebruch $\chi _y$ genus of these torus manifolds. We show that they have (invariant) almost complex structure if they admit positive omniorientation. We give examples of almost complex manifolds that do not admit a complex structure. When the dimension is four, we calculate the homology groups and describe a method for computing the cohomology ring.References
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Additional Information
- Mainak Poddar
- Affiliation: Departamento de Matemáticas, Universidad de los Andes, Bogota, Colombia
- Email: mainakp@gmail.com
- Soumen Sarkar
- Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea
- Email: soumensarkar20@gmail.com
- Received by editor(s): September 28, 2011
- Received by editor(s) in revised form: July 11, 2012, and July 18, 2013
- Published electronically: November 24, 2014
- Additional Notes: The first author was partially supported by the Proyecto de investigaciones grant from the Universidad de los Andes
The second author was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 2012-0000795) - Communicated by: Daniel Ruberman
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1797-1811
- MSC (2010): Primary 57R17, 57R91
- DOI: https://doi.org/10.1090/S0002-9939-2014-12075-2
- MathSciNet review: 3314091