Topological obstructions to totally skew embeddings

Authors:
Đorđe Baralić, Branislav Prvulović, Gordana Stojanović, Siniša Vrećica and Rade Živaljević

Journal:
Trans. Amer. Math. Soc. **364** (2012), 2213-2226

MSC (2010):
Primary 57R40; Secondary 55R40, 57R20

Published electronically:
October 21, 2011

MathSciNet review:
2869204

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Abstract | References | Similar Articles | Additional Information

Abstract: Following Ghomi and Tabachnikov's 2008 work, we study the invariant defined as the smallest dimension such that there exists a *totally skew* embedding of a smooth manifold in . This problem is naturally related to the question of estimating the geometric dimension of the stable normal bundle of the configuration space of ordered pairs of distinct points in . We demonstrate that in a number of interesting cases the lower bounds on obtained by this method are quite accurate and very close to the best known general upper bound established by Ghomi and Tabachnikov. We also provide some evidence for the conjecture that for every -dimensional, compact smooth manifold ,

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Additional Information

**Đorđe Baralić**

Affiliation:
Mathematical Institute, Serbian Academy of Sciences & Arts, Kneza Mihaila 36, p.p. 367, 11001 Belgrade, Serbia

Email:
djbaralic@mi.sanu.ac.rs

**Branislav Prvulović**

Affiliation:
Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia

Email:
bane@matf.bg.ac.rs

**Gordana Stojanović**

Affiliation:
Mathematical Institute, Serbian Academy of Sciences & Arts, Kneza Mihaila 36, p.p. 367, 11001 Belgrade, Serbia

Email:
golence@gmail.com

**Siniša Vrećica**

Affiliation:
Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia

Email:
vrecica@matf.bg.ac.rs

**Rade Živaljević**

Affiliation:
Mathematical Institute, Serbian Academy of Sciences & Arts, Kneza Mihaila 36, p.p. 367, 11001 Belgrade, Serbia

Email:
rade@mi.sanu.ac.rs

DOI:
http://dx.doi.org/10.1090/S0002-9947-2011-05499-1

Received by editor(s):
June 30, 2010

Received by editor(s) in revised form:
October 18, 2010

Published electronically:
October 21, 2011

Additional Notes:
This research was supported by the Grants 174020 and 174034 of the Ministry for Science and Technological Development of Serbia

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.