Twisted Homology of Configuration Spaces and Homology of Spaces of Equivariant Maps

Publication type Article
Status Published
Affiliation: Steklov Mathematical Institute, RAS
Address: Russian Federation
Journal nameDoklady Akademii nauk
EditionVolume 483 Issue 6

Abstract. We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres Sm ! SM, m < M, and of the stable homology of spaces of non-resultant polynomial maps Rm+1 ! RM+1. Also, we calculate the homology of spaces of Zr-equivariant maps of odd-dimensional spheres, and discuss further generalizations.

Publication date26.12.2018
Cite   Download pdf To download PDF you should sign in
Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

views: 1393

Readers community rating: votes 0

1. Anderson D.W A generalization of the Eilenberg-Moore spectral sequence // Bull. AMS. 1972. V. 1. P. 784-786.

2. Arnol'd V.I. O nekotorykh topologicheskikh invariantakh algebraicheskikh funktsij // Tr. MMO. 1970. T. 21. S. 27-46.

3. Cohen F.R., Cohen R.L., Mann B.M., Milgram R.L The topology of rational functions and divisors of surfaces // Acta Math. 1991. V. 166. P. 163-221.

4. Kozlowski A, Yamaguchi K. Topology of complements of discriminants and resultants // J. Math. Soc. Japan. 2000. V. 52. P. 949-959.

5. Kozlowski A., Yamaguchi K. Simplicial resolutions and spaces of algebraic maps between real projective spaces // Topology Appl. 2013. V. 160. № 1. P. 87-98.

6. Milnor J.W. Lectures on the h-cobordism theorem. Princeton Univ. Press, 1965.

7. Vassiliev V.A. Complements of discriminants of smooth maps: topology and applications. Providence (RI): Amer. Math. Soc. 1992.

8. Vasil'ev V.A. Ratsional'nye gomologii poryadkovogo kompleksa mnozhestv nulej odnorodnykh kvadratichnykh polinomial'nykh sistem v R3 // Tr. Mat. In-ta RAN. 2015. T. 290.

9. Vasil'ev V.A. Gruppy gomologij prostranstv nerezul'tantnykh sistem kvadratichnykh polinomov v R3 // Izv. RAN. Ser. mat. 2016. T. 80. № 4.

10. Vasil'ev V.A. Stabil'nye kogomologii prostranstv nerezul'tantnykh polinomial'nykh sistem v R3 // Dokl. RAN. 2017. T. 477. № 6.

11. Vasil'ev V.A. Stabil'nye kogomologii prostranstv nerezul'tantnykh sistem odnorodnykh polinomov v Rn // Dokl. RAN. 2018. V. 481. № 3.

12. Vassiliev V.A. Homology of the complex of not 2-divisible partitions // arXiv: 1807.05742.

Система Orphus