Volume 18, issue 1 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Rational smoothness, cellular decompositions and GKM theory

Richard Gonzales

Geometry & Topology 18 (2014) 291–326
Bibliography
1 V Alexeev, M Brion, Stable reductive varieties, II: Projective case, Adv. Math. 184 (2004) 380 MR2054021
2 A Arabia, Classes d'Euler équivariantes et points rationnellement lisses, Ann. Inst. Fourier 48 (1998) 861 MR1644106
3 M F Atiyah, Elliptic operators and compact groups, Lecture Notes in Mathematics 401, Springer (1974) MR0482866
4 M F Atiyah, G B Segal, The index of elliptic operators, II, Ann. of Math. 87 (1968) 531 MR0236951
5 A Białynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973) 480 MR0366940
6 A Białynicki-Birula, Some properties of the decompositions of algebraic varieties determined by actions of a torus, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976) 667 MR0453766
7 A Borel, Seminar on transformation groups, Annals of Mathematics Studies 46, Princeton Univ. Press (1960) MR0116341
8 L A Borisov, L Chen, G G Smith, The orbifold Chow ring of toric Deligne–Mumford stacks, J. Amer. Math. Soc. 18 (2005) 193 MR2114820
9 M Brion, Equivariant Chow groups for torus actions, Transform. Groups 2 (1997) 225 MR1466694
10 M Brion, The behaviour at infinity of the Bruhat decomposition, Comment. Math. Helv. 73 (1998) 137 MR1610599
11 M Brion, Equivariant cohomology and equivariant intersection theory, from: "Representation theories and algebraic geometry" (editors A Broer, G Sabidussi), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Kluwer Acad. Publ. (1998) 1 MR1649623
12 M Brion, Rational smoothness and fixed points of torus actions, Transform. Groups 4 (1999) 127 MR1712861
13 M Brion, Poincaré duality and equivariant (co)homology, Michigan Math. J. 48 (2000) 77 MR1786481
14 M Brion, Local structure of algebraic monoids, Mosc. Math. J. 8 (2008) 647, 846 MR2499350
15 J B Carrell, The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties, from: "Algebraic groups and their generalizations: Classical methods" (editors W J Haboush, B J Parshall), Proc. Sympos. Pure Math. 56, Amer. Math. Soc. (1994) 53 MR1278700
16 T Chang, T Skjelbred, The topological Schur lemma and related results, Ann. of Math. 100 (1974) 307 MR0375357
17 N Chriss, V Ginzburg, Representation theory and complex geometry, Birkhäuser (1997) MR1433132
18 V I Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978) 85 MR495499
19 A Dimca, Singularities and topology of hypersurfaces, Universitext, Springer (1992) MR1194180
20 R Gonzales, Equivariant cohomology of rationally smooth group embeddings arXiv:1112.1365
21 M Goresky, R Kottwitz, R MacPherson, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1998) 25 MR1489894
22 V Guillemin, M Kogan, Morse theory on Hamiltonian $G$–spaces and equivariant $K$–theory, J. Differential Geom. 66 (2004) 345 MR2106470
23 M Harada, A Henriques, T S Holm, Computation of generalized equivariant cohomologies of Kac–Moody flag varieties, Adv. Math. 197 (2005) 198 MR2166181
24 R Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer (1977) MR0463157
25 W y Hsiang, Cohomology theory of topological transformation groups, Ergeb. Math. Grenzgeb. 85, Springer (1975) MR0423384
26 F Kirwan, Intersection homology and torus actions, J. Amer. Math. Soc. 1 (1988) 385 MR928263
27 C McCrory, A characterization of homology manifolds, J. London Math. Soc. 16 (1977) 149 MR0445506
28 J Milnor, On the $3$–dimensional Brieskorn manifolds $M(p,q,r)$, from: "Knots, groups, and $3$–manifolds (Papers dedicated to the memory of R H Fox)" (editor L P Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 175 MR0418127
29 C A M Peters, J H M Steenbrink, Mixed Hodge structures, Ergeb. Math. Grenzgeb. 52, Springer (2008) MR2393625
30 D Quillen, The spectrum of an equivariant cohomology ring, I, II, Ann. of Math. 94 (1971) 549, 573 MR0298694
31 L E Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences 134, Springer (2005) MR2134980
32 L E Renner, The $H$–polynomial of a semisimple monoid, J. Algebra 319 (2008) 360 MR2378076
33 L E Renner, Descent systems for Bruhat posets, J. Algebraic Combin. 29 (2009) 413 MR2506714
34 L E Renner, Rationally smooth algebraic monoids, Semigroup Forum 78 (2009) 384 MR2511774
35 L E Renner, The $H$–polynomial of an irreducible representation, J. Algebra 332 (2011) 159 MR2774683
36 L Scull, Equivariant formality for actions of torus groups, Canad. J. Math. 56 (2004) 1290 MR2102634
37 G Segal, Equivariant $K$–theory, Inst. Hautes Études Sci. Publ. Math. (1968) 129 MR0234452
38 I R Shafarevich, Basic algebraic geometry, 1: Varieties in projective space, Springer (1994) MR1328833
39 H Sumihiro, Equivariant completion, Journal Math. Kyoto Univ. 14 (1974) 1 MR0337963
40 V Uma, Equivariant $K$–theory of compactifications of algebraic groups, Transform. Groups 12 (2007) 371 MR2323687
41 G Vezzosi, A Vistoli, Higher algebraic $K$–theory for actions of diagonalizable groups, Invent. Math. 153 (2003) 1 MR1990666
42 A Weber, Formality of equivariant intersection cohomology of algebraic varieties, Proc. Amer. Math. Soc. 131 (2003) 2633 MR1974316