Immersions of RP2e−1

Davis, Donald M; Dula, Giora; González, Jesús; Mahowald, Mark

doi:10.2140/agt.2008.8.997

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Immersions of $RP^{2^e-1}$

Donald M Davis, Giora Dula, Jesús González and Mark Mahowald

Algebraic & Geometric Topology 8 (2008) 997–1030

DOI: 10.2140/agt.2008.8.997

Abstract

We prove that $R P^{2^{e} - 1}$ can be immersed in $ℝ^{2^{e + 1} - e - 7}$ provided $e \geq 7$ . If $e \geq 14$ , this is 1 better than previously known immersions. Our method is primarily an induction on geometric dimension, with compatibility of liftings being a central issue.

Keywords

immersions, real projective space

Mathematical Subject Classification 2000

Primary: 57N35

Secondary: 55S40

References

Publication

Received: 11 January 2007

Revised: 23 May 2008

Accepted: 23 May 2008

Published: 5 July 2008

Authors

Donald M Davis
Lehigh University Bethlehem, PA 18015 USA
http://www.lehigh.edu/~dmd1
Giora Dula
Netanya College Netanya 42365 Israel

Jesús González
Departamento de Matemáticas Centro de Investigación y de Estudios Avanzados del IPN México DF 07000 México

Mark Mahowald
Northwestern University Evanston, IL 60208 USA

Volume 8, issue 2 (2008)