Graded algebras having a unique rational homotopy type

Shiga, Hiroo; Yagita, Nobuaki

doi:10.1090/S0002-9939-1982-0660618-7

Graded algebras having a unique rational homotopy type
HTML articles powered by AMS MathViewer

by Hiroo Shiga and Nobuaki Yagita

Proc. Amer. Math. Soc. 85 (1982), 623-632

DOI: https://doi.org/10.1090/S0002-9939-1982-0660618-7

PDF | Request permission

Abstract:

We consider the problem for which graded algebra ${A^* }$ complexes such that ${H^*}(K,Q) \simeq {A^*}$ is unique up to homotopy type. A necessary and sufficient condition is given using formal minimal model of ${A^*}$.

References

Richard Body, Regular rational homotopy types, Comment. Math. Helv. 50 (1975), 89–92. MR 380782, DOI 10.1007/BF02565736
Pierre Deligne, Phillip Griffiths, John Morgan, and Dennis Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), no. 3, 245–274. MR 382702, DOI 10.1007/BF01389853
Mamoru Mimura and Hirosi Toda, On $p$-equivalences and $p$-universal spaces, Comment. Math. Helv. 46 (1971), 87–97. MR 285007, DOI 10.1007/BF02566829
Daniel Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295. MR 258031, DOI 10.2307/1970725
Hiroo Shiga, Rational homotopy type and self-maps, J. Math. Soc. Japan 31 (1979), no. 3, 427–434. MR 535089, DOI 10.2969/jmsj/03130427
D. Sullivan, Differential forms and the topology of manifolds, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 37–49. MR 0370611
Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978). MR 646078
Stephen Halperin and James Stasheff, Obstructions to homotopy equivalences, Adv. in Math. 32 (1979), no. 3, 233–279. MR 539532, DOI 10.1016/0001-8708(79)90043-4