Geodesic
Resolutions of p–stratifolds with isolated singularities
Grinberg, Anna1
1Department of Mathematics, UC San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, USA
Algebraic and Geometric Topology, Tome 3 (2003) no. 2, pp. 1051-1078
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Recently M Kreck introduced a class of stratified spaces called p–stratifolds [M Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p–stratifolds analogously to resolutions of algebraic varieties. In this note we study a very special case of resolutions, so called optimal resolutions, for p–stratifolds with isolated singularities. We give necessary and sufficient conditions for existence and analyze their classification.

DOI : 10.2140/agt.2003.3.1051
Keywords: stratifold, stratified space, resolution, isolated singularity

Grinberg, Anna  1

1 Department of Mathematics, UC San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, USA 
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Grinberg, Anna. Resolutions of p–stratifolds with isolated singularities. Algebraic and Geometric Topology, Tome 3 (2003) no. 2, pp. 1051-1078. doi: 10.2140/agt.2003.3.1051

[1] S Akbulut, H King, The topology of real algebraic sets, Enseign. Math. $(2)$ 29 (1983) 221

[2] H J Baues, Obstruction theory on homotopy classification of maps, Lecture Notes in Mathematics 628, Springer (1977)

[3] R Benedetti, J J Risler, Real algebraic and semi-algebraic sets, Actualités Mathématiques., Hermann (1990) 340

[4] T Bröcker, T Tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics 98, Springer (1985)

[5] P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete 33, Academic Press (1964)

[6] M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357

[7] M W Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer (1976)

[8] A Haefliger, Differentiable imbeddings, Bull. Amer. Math. Soc. 67 (1961) 109

[9] H Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero I, II, Ann. of Math. $(2)$ 79 (1964) 109

[10] M A Kervaire, Some nonstable homotopy groups of Lie groups, Illinois J. Math. 4 (1960) 161

[11] M Kreck, Surgery and duality, Ann. of Math. $(2)$ 149 (1999) 707

[12] M Kreck, Differential algebraic topology, preprint

[13] M Kreck, Stratifolds, preprint

[14] J Milnor, A procedure for killing homotopy groups of differentiable manifolds., from: "Proc. Sympos. Pure Math., Vol III", American Mathematical Society (1961) 39

[15] J Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press (1963)

[16] J W Milnor, Remarks concerning spin manifolds, from: "Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse)", Princeton Univ. Press (1965) 55

[17] J Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies 61, Princeton University Press (1968)

[18] R E Stong, Notes on cobordism theory, Mathematical notes, Princeton University Press (1968)

[19] N Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series 14, Princeton University Press (1951)

[20] R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17

[21] C T C Wall, Classification of $(n-1)$–connected $2n$–manifolds, Ann. of Math. $(2)$ 75 (1962) 163

[22] C T C Wall, Surgery on compact manifolds, London Mathematical Society Monographs 1, Academic Press (1970)

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