# Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Annales de l'institut Fourier (1972)

- Volume: 22, Issue: 1, page 271-286
- ISSN: 0373-0956

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topSato, Hajime. "Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds." Annales de l'institut Fourier 22.1 (1972): 271-286. <http://eudml.org/doc/74068>.

@article{Sato1972,

abstract = {We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold $M^n$. The main theorem says that there is a unique obstruction element in $H_\{n-4\}(M,\{\cal H\}^3)$, where $\{\cal H\}^3$ is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and $M$ is compact, we obtain a PL-manifold which is simple homotopy equivalent to $M$.},

author = {Sato, Hajime},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {1},

pages = {271-286},

publisher = {Association des Annales de l'Institut Fourier},

title = {Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds},

url = {http://eudml.org/doc/74068},

volume = {22},

year = {1972},

}

TY - JOUR

AU - Sato, Hajime

TI - Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

JO - Annales de l'institut Fourier

PY - 1972

PB - Association des Annales de l'Institut Fourier

VL - 22

IS - 1

SP - 271

EP - 286

AB - We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold $M^n$. The main theorem says that there is a unique obstruction element in $H_{n-4}(M,{\cal H}^3)$, where ${\cal H}^3$ is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and $M$ is compact, we obtain a PL-manifold which is simple homotopy equivalent to $M$.

LA - eng

UR - http://eudml.org/doc/74068

ER -

## References

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- [5] M. KERVAIRE et J. MILNOR, Groups of homotopy spheres I, Ann. Math. 77 (1963), 504-537. Zbl0115.40505MR26 #5584
- [6] I. TAMURA, Variety of manifolds (in Japanese), Sûgaku 21 (1969), 275-285.
- [7] G.W. WHITEHEAD, Generalized homology theory, Trans. Amer. Math. Soc. 102 (1962), 227-283. Zbl0124.38302MR25 #573
- [8] J.H.C. WHITEHEAD, Simple homotopy types, Amer. J. Math. 72 (1950), 1-57. Zbl0040.38901MR11,735c
- [9] D. SULLIVAN, Geometric periodicity and the invariants of manifolds, Lecture Notes in Math. Springer Verlag 197, 44-75. Zbl0224.57002MR44 #2236

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