Results 11  20
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84
Topological 4manifolds with geometrically 2dimensional fundamental groups
, 2009
"... Closed oriented 4manifolds with the same geometrically 2dimensional fundamental group (satisfying certain properties) are classified up to scobordism by their w2type, equivariant intersection form and the KirbySiebenmann invariant. As an application, we obtain a complete homeomorphism classific ..."
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Cited by 7 (2 self)
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Closed oriented 4manifolds with the same geometrically 2dimensional fundamental group (satisfying certain properties) are classified up to scobordism by their w2type, equivariant intersection form and the KirbySiebenmann invariant. As an application, we obtain a complete homeomorphism classification of closed oriented 4manifolds with solvable BaumslagSolitar fundamental groups, including a precise realization result.
Some examples of free actions on products of spheres
 TOPOLOGY
, 2006
"... If G1 and G2 are finite groups with periodic Tate cohomology, then G1 × G2 acts freely and smoothly on some product S n × S n. ..."
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Cited by 7 (6 self)
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If G1 and G2 are finite groups with periodic Tate cohomology, then G1 × G2 acts freely and smoothly on some product S n × S n.
HOMOLOGY SURGERY AND INVARIANTS OF 3MANIFOLDS
"... Abstract. We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of πalgebraicallysplit links in 3manifolds with fundamental group π. Using this class of links, we define a theory of finite type inva ..."
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Cited by 6 (2 self)
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Abstract. We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of πalgebraicallysplit links in 3manifolds with fundamental group π. Using this class of links, we define a theory of finite type invariants of 3manifolds in such a way that invariants of degree 0 are precisely those of conventional algebraic topology and surgery theory. When finite type invariants are reformulated in terms of clovers, we deduce upper bounds for the number of invariants in terms of πdecorated trivalent graphs. We also consider an associated notion of surgery equivalence of πalgebraically split links and prove a classification theorem using a generalization of Milnor’s ¯µinvariants to this class of links. 1.
Poincaré Sheaves on Topological Spaces
 Trans. Amer. Math. Soc
"... We define the notion of a Poincar'e complex of sheaves over a topological space. Global surgery invariants of spaces and maps are expressed as the assembly of locally defined surgery invariants. For simplicial complexes we recover the theory of Poincar'e cycles of Ranicki. For more general ..."
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Cited by 5 (1 self)
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We define the notion of a Poincar'e complex of sheaves over a topological space. Global surgery invariants of spaces and maps are expressed as the assembly of locally defined surgery invariants. For simplicial complexes we recover the theory of Poincar'e cycles of Ranicki. For more general spaces we obtain local surgery invariants in the absence of triangulations. 1.
Codimension 2 embeddings, algebraic surgery and Seifert forms, preprint 2012, arxiv
 1211.5964. OF THE MOD 2 SPECTRUM 13
"... Abstract. We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings M m ⊂ N m+2, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of algebraic Poincaré pairs, which is then applied to describe t ..."
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Cited by 5 (4 self)
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Abstract. We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings M m ⊂ N m+2, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of algebraic Poincaré pairs, which is then applied to describe the behaviour on the chain level of Seifert surfaces of embeddings M 2n−1 ⊂ S 2n+1 under isotopy and cobordism. The second main result is that the Sequivalence class of a Seifert form is an isotopy invariant of the embedding, generalizing the Murasugi–Levine result for knots and links. The third main result is a generalized Murasugi–Kawauchi inequality giving an upper bound on the difference of the Levine–Tristram signatures of cobordant embeddings.
Circle valued Morse theory and Novikov homology
"... Traditional Morse theory deals with real valued functions f : M R and ordinary homology H (M ). The critical points of a Morse function f generate the MorseSmale (f) over Z, using the gradient flow to define the differentials. The isomorphism H (M) imposes homological restrictions on real valued Mo ..."
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Cited by 5 (0 self)
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Traditional Morse theory deals with real valued functions f : M R and ordinary homology H (M ). The critical points of a Morse function f generate the MorseSmale (f) over Z, using the gradient flow to define the differentials. The isomorphism H (M) imposes homological restrictions on real valued Morse functions. There is also a universal coefficient version of the MorseSmale complex, involving the universal cover M and the fundamental group ring Z[# 1 (M )].
On two results about fibrations
 Manuscripta Math
, 1997
"... Using equivariant methods, we provide straightforward proofs of a result of Chachdlski and a result of Spivak about fibrations. Let h., denote a reduced homology theory on the category of based spaces and let h, denote the corresponding extension to an unreduced homology theory on the category of un ..."
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Cited by 4 (4 self)
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Using equivariant methods, we provide straightforward proofs of a result of Chachdlski and a result of Spivak about fibrations. Let h., denote a reduced homology theory on the category of based spaces and let h, denote the corresponding extension to an unreduced homology theory on the category of unbased spaces given by h,(X) = h,(X+), where X+ denotes X with the addition of a disjoint basepoint.
Signatures and higher signatures on S1quotients
, 1998
"... Abstract. We define and study the signature, bAgenus and higher signatures of the quotient space of an S1action on a closed oriented manifold. We give applications to questions of positive scalar curvature and to an Equivariant Novikov Conjecture. 1. ..."
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Cited by 2 (0 self)
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Abstract. We define and study the signature, bAgenus and higher signatures of the quotient space of an S1action on a closed oriented manifold. We give applications to questions of positive scalar curvature and to an Equivariant Novikov Conjecture. 1.
MULTIPLICATIVE PROPERTIES OF QUINN SPECTRA
, 907
"... Abstract. We give a simple sufficient condition for Quinn’s “bordismtype spectra ” to be weakly equivalent to strictly associative ring spectra. We also show that Poincaré bordism and symmetric Ltheory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements invo ..."
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Cited by 2 (2 self)
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Abstract. We give a simple sufficient condition for Quinn’s “bordismtype spectra ” to be weakly equivalent to strictly associative ring spectra. We also show that Poincaré bordism and symmetric Ltheory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn’s functor from bordismtype theories to spectra lifts to the category of symmetric spectra. We also give a new account of the foundations.
POINCARÉ DUALITY COMPLEXES IN DIMENSION FOUR
, 2008
"... We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD^4complexes. Generalizing Turaev’s fundamental triples of PD³complexes we introduce fundamental triples for PD^ncomplexes and show that two PD^ncomplexes are orientedly homotopy eq ..."
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We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD^4complexes. Generalizing Turaev’s fundamental triples of PD³complexes we introduce fundamental triples for PD^ncomplexes and show that two PD^ncomplexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n–dimensional manifolds.