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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 RP2e−1 can be immersed in ℝ2e+1−e−7 provided e ≥ 7. If e ≥ 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