Geodesic
Rational analogs of projective planes
Su, Zhixu1
1Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 421-438
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

In this paper, we study the existence of high-dimensional, closed, smooth manifolds whose rational homotopy type resembles that of a projective plane. Applying rational surgery, the problem can be reduced to finding possible Pontryagin numbers satisfying the Hirzebruch signature formula and a set of congruence relations, which turns out to be equivalent to finding solutions to a system of Diophantine equations.

DOI : 10.2140/agt.2014.14.421
Classification : 57R20, 57R65, 57R67
Keywords: rational surgery, rational homotopy type, smooth manifold

Su, Zhixu  1

1 Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA 
@article{10_2140_agt_2014_14_421,
     author = {Su, Zhixu},
     title = {Rational analogs of projective planes},
     journal = {Algebraic and Geometric Topology},
     pages = {421--438},
     year = {2014},
     volume = {14},
     number = {1},
     doi = {10.2140/agt.2014.14.421},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.421/}
}
TY  - JOUR
AU  - Su, Zhixu
TI  - Rational analogs of projective planes
JO  - Algebraic and Geometric Topology
PY  - 2014
SP  - 421
EP  - 438
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.421/
DO  - 10.2140/agt.2014.14.421
ID  - 10_2140_agt_2014_14_421
ER  - 
%0 Journal Article
%A Su, Zhixu
%T Rational analogs of projective planes
%J Algebraic and Geometric Topology
%D 2014
%P 421-438
%V 14
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.421/
%R 10.2140/agt.2014.14.421
%F 10_2140_agt_2014_14_421
Su, Zhixu. Rational analogs of projective planes. Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 421-438. doi: 10.2140/agt.2014.14.421

[1] D R Anderson, On homotopy spheres bounding highly connected manifolds, Trans. Amer. Math. Soc. 139 (1969) 155

[2] J Barge, Structures différentiables sur les types d'homotopie rationnelle simplement connexes, Ann. Sci. École Norm. Sup. 9 (1976) 469

[3] I H Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, Annals of Mathematics Studies 92, Princeton Univ. Press (1979)

[4] J Milnor, Collected papers of John Milnor, III: Differential topology, Amer. Math. Soc. (2007)

[5] J Milnor, D Husemoller, Symmetric bilinear forms, Ergeb. Math. Grenzgeb. 73, Springer (1973)

[6] J W Milnor, J D Stasheff, Characteristic classes, Annals of Mathematics Studies 76, Princeton Univ. Press (1974)

[7] R E Stong, Relations among characteristic numbers, I, Topology 4 (1965) 267

[8] R E Stong, Notes on cobordism theory, Princeton Univ. Press (1968)

[9] Z Su, Rational homotopy type of manifolds, PhD thesis, Indiana University (2009)

[10] D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) 269

[11] L Taylor, B Williams, Local surgery: Foundations and applications, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 673

Cité par Sources :