scholarly journals Complete shrinking Ricci solitons have finite fundamental group

2007 ◽  
Vol 136 (05) ◽  
pp. 1803-1807 ◽  
Author(s):  
William Wylie
Keyword(s):  
Fundamental Group ◽  
Ricci Solitons ◽  
Finite Fundamental Group

scholarly journals On macroscopic dimension of non-spin 4-manifolds

2020 ◽  
pp. 1-10
Author(s):  
Michelle Daher ◽  
Alexander Dranishnikov
Keyword(s):  
Fundamental Group ◽  
Universal Covering ◽  
Residually Finite ◽  
Finite Fundamental Group

We prove that for 4-manifolds [Formula: see text] with residually finite fundamental group and non-spin universal covering [Formula: see text], the inequality [Formula: see text] implies the inequality [Formula: see text]. This allows us to complete the proof of Gromov’s Conjecture for 4-manifolds with abelian fundamental group.

scholarly journals Surfaces with $K^2 \lt 3\chi$ and finite fundamental group

2007 ◽  
Vol 14 (6) ◽  
pp. 1081-1098 ◽  
Author(s):  
Ciro Ciliberto ◽  
Margarida Mendes Lopes ◽  
Rita Pardini
Keyword(s):  
Fundamental Group ◽  
Finite Fundamental Group

FIXED POINT FREE CIRCLE ACTIONS AND FINITENESS THEOREMS

2000 ◽  
Vol 02 (01) ◽  
pp. 75-86 ◽  
Author(s):  
FUQUAN FANG ◽  
XIAOCHUN RONG
Keyword(s):  
Fixed Point ◽  
Fundamental Group ◽  
Fundamental Groups ◽  
Vanishing Theorem ◽  
Fixed Point Set ◽  
Circle Actions ◽  
Finite Fundamental Group ◽  
Finiteness Theorems ◽  
Point Set ◽  
Simply Connected

We prove a vanishing theorem of certain cohomology classes for an 2n-manifold of finite fundamental group which admits a fixed point free circle action. In particular, it implies that any Tk-action on a compact symplectic manifold of finite fundamental group has a non-empty fixed point set. The vanishing theorem is used to prove two finiteness results in which no lower bound on volume is assumed. (i) The set of symplectic n-manifolds of finite fundamental groups with curvature, λ ≤ sec ≤ Λ, and diameter, diam ; ≤ d, contains only finitely many diffeomorphism types depending only on n, λ, Λ and d. (ii) The set of simply connected n-manifolds (n ≤ 6) with λ ≤ sec ≤ Λ and diam ≤ d contains only finitely many diffeomorphism types depending only on n, λ, Λ and d.

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