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Existence results of totally real immersions and embeddings into $ \mathbb{C}^N$


Authors: Marko Slapar and Rafael Torres
Journal: Proc. Amer. Math. Soc. 146 (2018), 5463-5473
MSC (2010): Primary 57R42, 32Q99
DOI: https://doi.org/10.1090/proc/14234
Published electronically: September 4, 2018
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Abstract: We prove that the existence of totally real immersions of manifolds is a closed property under cut-and-paste constructions along submanifolds including connected sums. We study the existence of totally real embeddings for simply connected $ 5$-manifolds and orientable $ 6$-manifolds and determine the diffeomorphism and homotopy types. We show that the fundamental group is not an obstruction for the existence of a totally real embedding for high-dimensional manifolds in contrast with the situation in dimension four.


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Marko Slapar
Affiliation: Faculty of Education, University of Ljubljana, Kardeljeva Poscad 16, 1000, Ljubljana, Slovenia – and – Institute of Mathematics, Physics and Mechanics, Jadranksa 19, 1000, Ljubljana, Slovenia
Email: marko.slapar@pef.uni-lj.si

Rafael Torres
Affiliation: Scuola Internazionale Superiori di Studi Avanzati (SISSA), Via Bonomea 265, 34136, Trieste, Italy
Email: rtorres@sissa.it

DOI: https://doi.org/10.1090/proc/14234
Received by editor(s): December 22, 2017
Received by editor(s) in revised form: March 22, 2018
Published electronically: September 4, 2018
Communicated by: Filippo Bracci
Article copyright: © Copyright 2018 American Mathematical Society

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