Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



Contractible polyhedra in products of trees and absolute retracts in products of dendrites

Authors: Sergey A. Melikhov and Justyna Zajac
Journal: Proc. Amer. Math. Soc. 141 (2013), 2519-2535
MSC (2010): Primary 54C25, 57Q35; Secondary 55P57, 06A07, 57M20, 55M15
Published electronically: February 21, 2013
MathSciNet review: 3043032
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that a compact $ n$-polyhedron PL embeds in a product of $ n$ trees if and only if it collapses onto an $ (n-1)$-polyhedron. If the $ n$-polyhedron is contractible and $ n\ne 3$ (or $ n=3$ and the Andrews-Curtis Conjecture holds), the product of trees may be assumed to collapse onto the image of the embedding.

In contrast, there exists a $ 2$-dimensional compact absolute retract $ X$ such that $ X\times I^k$ does not embed in any product of $ 2+k$ dendrites for each $ k$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 54C25, 57Q35, 55P57, 06A07, 57M20, 55M15

Retrieve articles in all journals with MSC (2010): 54C25, 57Q35, 55P57, 06A07, 57M20, 55M15

Additional Information

Sergey A. Melikhov
Affiliation: Steklov Mathematical Institute of the Russian Academy of Sciences, ul. Gubkina 8, Moscow 119991, Russia

Justyna Zajac
Affiliation: Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Received by editor(s): May 17, 2011
Received by editor(s) in revised form: September 29, 2011, October 7, 2011, and October 8, 2011
Published electronically: February 21, 2013
Additional Notes: The first author is supported by Russian Foundation for Basic Research Grant No. 11-01-00822, Russian Government project 11.G34.31.0053 and Federal Program “Scientific and Scientific-Pedagogical Staff of Innovative Russia” 2009–2013
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia