Algebraic & Geometric Topology Volume 24, issue 4 (2024)

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Integral generalized equivariant cohomologies of weighted Grassmann orbifolds

Koushik Brahma and Soumen Sarkar

Algebraic & Geometric Topology 24 (2024) 2209–2244

DOI: 10.2140/agt.2024.24.2209

Bibliography

1	H Abe, T Matsumura, Equivariant cohomology of weighted Grassmannians and weighted Schubert classes, Int. Math. Res. Not. 2015 (2015) 2499 MR3344679
2	A Adem, J Leida, Y Ruan, Orbifolds and stringy topology, 171, Cambridge Univ. Press (2007) MR2359514
3	A Bahri, M Franz, N Ray, The equivariant cohomology ring of weighted projective space, Math. Proc. Cambridge Philos. Soc. 146 (2009) 395 MR2475973
4	A Bahri, D Notbohm, S Sarkar, J Song, On integral cohomology of certain orbifolds, Int. Math. Res. Not. 2021 (2021) 4140 MR4230390
5	W L Baily Jr., The decomposition theorem for V –manifolds, Amer. J. Math. 78 (1956) 862 MR0100103
6	W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
7	A Corti, M Reid, Weighted Grassmannians, from: "Algebraic geometry" (editors M C Beltrametti, F Catanese, C Ciliberto, A Lanteri, C Pedrini), de Gruyter (2002) 141 MR1954062
8	A Darby, S Kuroki, J Song, Equivariant cohomology of torus orbifolds, Canad. J. Math. 74 (2022) 299 MR4410992
9	T tom Dieck, Bordism of G–manifolds and integrality theorems, Topology 9 (1970) 345 MR0266241
10	F Galaz-García, M Kerin, M Radeschi, M Wiemeler, Torus orbifolds, slice-maximal torus actions, and rational ellipticity, Int. Math. Res. Not. 2018 (2018) 5786 MR3862119
11	R M Goresky, Triangulation of stratified objects, Proc. Amer. Math. Soc. 72 (1978) 193 MR0500991
12	V Guillemin, C Zara, 1–skeleta, Betti numbers, and equivariant cohomology, Duke Math. J. 107 (2001) 283 MR1823050
13	B Hanke, Geometric versus homotopy theoretic equivariant bordism, Math. Ann. 332 (2005) 677 MR2181767
14	M Harada, A Henriques, T S Holm, Computation of generalized equivariant cohomologies of Kac–Moody flag varieties, Adv. Math. 197 (2005) 198 MR2166181
15	M Harada, T S Holm, N Ray, G Williams, The equivariant K–theory and cobordism rings of divisive weighted projective spaces, Tohoku Math. J. 68 (2016) 487 MR3605445
16	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
17	D Husemoller, Fibre bundles, McGraw-Hill (1966) MR229247
18	X Jiao, J Peng, Pseudo-holomorphic curves in complex Grassmann manifolds, Trans. Amer. Math. Soc. 355 (2003) 3715 MR1990170
19	T Kawasaki, Cohomology of twisted projective spaces and lens complexes, Math. Ann. 206 (1973) 243 MR0339247
20	A Knutson, T Tao, Puzzles and (equivariant) cohomology of Grassmannians, Duke Math. J. 119 (2003) 221 MR1997946
21	D Laksov, Algebraic cycles on Grassmann varieties, Adv. Math. 9 (1972) 267 MR0318145
22	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
23	J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
24	A Mukherjee, Differential topology, Hindustan (2015) MR3379695
25	M Poddar, S Sarkar, On quasitoric orbifolds, Osaka J. Math. 47 (2010) 1055 MR2791564
26	S Sarkar, J Song, GKM theory for orbifold stratified spaces and application to singular toric varieties, Topology Appl. 288 (2021) 107472 MR4186079
27	I Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 359 MR0079769
28	I Satake, The Gauss–Bonnet theorem for V –manifolds, J. Math. Soc. Japan 9 (1957) 464 MR0095520
29	G Segal, Equivariant K–theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 129 MR0234452
30	D P Sinha, Computations of complex equivariant bordism rings, Amer. J. Math. 123 (2001) 577 MR1844571
31	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)