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

 

Invariant points of maps
between Grassmannians


Authors: Kalyan Mukherjea and Parameswaran Sankaran
Journal: Proc. Amer. Math. Soc. 124 (1996), 649-653
MSC (1991): Primary 55M20, 54H25
MathSciNet review: 1301041
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Abstract: We show that for a very large class of integers $l<k<n$ and any map $f\colon G_k(\mathbb R^n)\to G_l(\mathbb R^n)$ between Grassmannians, there is some $k$-plane of $\mathbb R^n$ which is mapped into a subspace of itself.


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Additional Information

Kalyan Mukherjea
Affiliation: SPIC Science Foundation, 92 G. N. Chetty Road, T. Nagar, Madras 600017, India
Email: kalyan@isical.ernet.in

Parameswaran Sankaran
Affiliation: SPIC Science Foundation, 92 G. N. Chetty Road, T. Nagar, Madras 600017, India
Email: sankaran@ssf.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03152-8
PII: S 0002-9939(96)03152-8
Keywords: Fixed-point theory, Grassmannians, invariant points, mod 2 Steenrod algebra
Received by editor(s): April 5, 1994
Received by editor(s) in revised form: September 21, 1994
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society