L-classes of rational homology manifolds

1972 ◽  
pp. 1-31
Author(s):  
Don Bernard Zagier
Keyword(s):  
Rational Homology ◽  
Homology Manifolds

Euler classes of vector bundles over manifolds

2021 ◽  
Vol 71 (1) ◽  
pp. 199-210
Author(s):  
Aniruddha C. Naolekar
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Euler Class ◽  
Homology Sphere ◽  
Rational Homology ◽  
Rational Homology Sphere ◽  
Orientable Manifolds

Abstract Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k-manifolds X with the property that for any oriented vector bundle α over X, the Euler class e(α) = 0. We show that if X ∈ 𝓔2n+1 is orientable, then X is a rational homology sphere and π 1(X) is perfect. We also show that 𝓔8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .

scholarly journals Topology of homology manifolds

1993 ◽  
Vol 28 (2) ◽  
pp. 324-329 ◽  
Author(s):  
J. Bryant ◽  
S. Ferry ◽  
W. Mio ◽  
S. Weinberger
Keyword(s):  
Homology Manifolds

IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE

2008 ◽  
Vol 17 (10) ◽  
pp. 1199-1221 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YASUSHI MIZUSAWA
Keyword(s):  
Number Field ◽  
Class Number ◽  
Homology Sphere ◽  
Rational Homology ◽  
Homology Groups ◽  
Cyclic Covers ◽  
Class Number Formula ◽  
Number Formula ◽  
Iwasawa Invariants ◽  
Rational Homology Sphere

Based on the analogy between links and primes, we present an analogue of the Iwasawa's class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.

Resolutions of Homology Manifolds: A Classification Theorem

1975 ◽  
Vol s2-11 (4) ◽  
pp. 474-480 ◽  
Author(s):  
Allan L. Edmonds ◽  
Ronald J. Stern
Keyword(s):  
Classification Theorem ◽  
Homology Manifolds
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