Mod 2 degree and a generalized No Retraction Theorem

Mathematische Nachrichten

Volumn 279, Issue 5-6, 2006, Pages 490-494

  Bloch, Ethan D ^a  

^a BARD COLLEGE   (United States)

Author keywords

Degree of a map; No Retraction Theorem; Sperner's Lemma

Indexed keywords

EID: 33645668592     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200310373     Document Type: Article

References (17)

1. A. B. Brown and S. S. Cairns, Strengthening of Sperner's lemma applied to homology theory, Proc. Natl. Acad. Sci. USA 47, 113-114 (1961).
2. R H Bing, The elusive fixed point property, Amer. Math. Monthly 76, 119-132 (1969).
3. K. Fan, Simplicial maps of pseudomanifolds, Ann. New York Acad. Sci. 31, 125-130 (1970).
4. R. M. Freund, Combinatorial analogs of Brouwer's fixed-point theorem on a bounded polyhedron, J. Combin. Theory Ser. B 47, 192-219 (1989).
5. F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
6. M. W. Hirsch, A proof of the nonretractibility of a cell onto its boundary, Proc. Amer. Math. Soc. 14, 364-365 (1963).
7. K. Joshi, Mistake in Hirsch's proof of the Brouwer fixed point theorem, Proc. Amer. Math. Soc. 128, No. 5, 1523-1525 (2000).
8. J. W. Milnor, Analytic proofs of the "hairy ball theorem" and the Brouwer fixed point theorem, Amer. Math. Monthly 85, 521-524 (1978).
9. C. A. Rogers, A less strange version of Milnor's proof of Brouwer's fixed-point theorem, Amer. Math. Monthly 87, 525-527 (1980).
10. D. E. Sanderson, An elementary romp through some advanced euclidean topology, Topology Proc. 1, 79-89 (1976).
11. Yu. A. Shashkin, Local degrees of simplicial mappings, Publ. Math. Debrecen 45, 407-413 (1994).
12. Yu. A. Shashkin, Remark on local degrees of simplicial mappings, Publ. Math. Debrecen 49, 301-304 (1996).
13. K. Sieklucki, An inductive proof of the nonretractibility of a cell onto its boundary, Comment. Math. Prace Mat. 23, 129-131 (1983).
14. H. Sies, Topological degree and sperner's lemma, Fund. Math. 118, No. 2, 135-149 (1983).
15. E. Spanier, Algebraic Topology (McGraw-Hill, New York, 1966).
16. A. W. Tucker, On Sperner's lemma and another combinatorial lemma, Proceedings of the Second International Conference on Combinatorial Mathematics, New York, 1978, Annals of the New York Academy of Sciences Vol. 319 (New York Acad. Sci., New York, 1979), pp. 536-539.
17. E. C. Zeeman, Relative simplicial approximation, Math. Proc. Cambridge Philos. Soc. 60, 39-43 (1964).