NDLI: A Note on the Homotopy Type of the Alexander Dual

Content Provider	Springer Nature Link
Author	Minian, Elías Gabriel Rodríguez, Jorge Tomás
Copyright Year	2014
Abstract	We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of $$K$$ does not determine the homotopy type of its dual $$K^$$ . We construct for each finitely presented group $$G$$ , a simply connected simplicial complex $$K$$ such that $$\pi _1(K^)=G$$ and study sufficient conditions on $$K$$ for $$K^*$$ to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute.
Ending Page	43
Page Count	10
Starting Page	34
File Format	PDF
ISSN	01795376
e-ISSN	14320444
Journal	Discrete & Computational Geometry
Issue Number	1
Volume Number	52
Language	English
Publisher	Springer US
Publisher Date	2014-07-09
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Partial order, general Computational Mathematics and Numerical Analysis Alexander duality Deleted joins Lattices Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. Simplicial complexes Abstract complexes Triangulating manifolds Polyhedral manifolds Classification of homotopy type Homotopy types General topology of complexes Combinatorics Bier spheres
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A note on the homotopy type of the Alexander dual

Some remarks on Morse theory for posets, homological Morse theory and finite manifolds

A Note on the Homotopy Type of the Alexander Dual

Non-homogeneous combinatorial manifolds

One-point reductions of finite spaces, h-regular CW-complexes and collapsibility

Random Simple-Homotopy Theory

Collapses, products and LC manifolds

Duality in Toric Topology

Non-homogeneous combinatorial manifolds

A Note on the Homotopy Type of the Alexander Dual

Similar Documents

A note on the homotopy type of the Alexander dual

Some remarks on Morse theory for posets, homological Morse theory and finite manifolds

A Note on the Homotopy Type of the Alexander Dual

Non-homogeneous combinatorial manifolds

One-point reductions of finite spaces, h-regular CW-complexes and collapsibility

Random Simple-Homotopy Theory

Collapses, products and LC manifolds

Duality in Toric Topology

Non-homogeneous combinatorial manifolds

A Note on the Homotopy Type of the Alexander Dual