Kreck, Matthias 1947
Overview
Works:  37 works in 111 publications in 2 languages and 1,459 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA613, 516.36 
Publication Timeline
.
Most widely held works by
Matthias Kreck
Bordism of diffeomorphisms and related topics by
Matthias Kreck(
Book
)
20 editions published between 1984 and 2008 in English and German and held by 359 WorldCat member libraries worldwide
20 editions published between 1984 and 2008 in English and German and held by 359 WorldCat member libraries worldwide
The Novikov conjecture : geometry and algebra by
Matthias Kreck(
Book
)
22 editions published in 2005 in English and held by 249 WorldCat member libraries worldwide
Manifolds are the central geometric objects in modern mathematics. An attempt to understand the nature of manifolds leads to many interesting questions. One of the most obvious questions is the following. Let M and N be manifolds: how can we decide whether M and N are ho topy equivalent or homeomorphic or di?eomorphic (if the manifolds are smooth)? The prototype of a beautiful answer is given by the Poincar´ e Conjecture. If n N is S ,the ndimensional sphere, and M is an arbitrary closed manifold, then n it is easy to decide whether M is homotopy equivalent to S . Thisisthecaseif and only if M is simply connected (assumingn> 1, the case n = 1 is trivial since 1 every closed connected 1dimensional manifold is di?eomorphic toS ) and has the n homology of S . The Poincar´eConjecture states that this is also su?cient for the n existenceof ahomeomorphism fromM toS . For n = 2this followsfromthewe known classi?cation of surfaces. Forn> 4 this was proved by Smale and Newman in the 1960s, Freedman solved the case in n = 4 in 1982 and recently Perelman announced a proof for n = 3, but this proof has still to be checked thoroughly by the experts. In the smooth category it is not true that manifolds homotopy n equivalent to S are di?eomorphic. The ?rst examples were published by Milnor in 1956 and together with Kervaire he analyzed the situation systematically in the 1960s
22 editions published in 2005 in English and held by 249 WorldCat member libraries worldwide
Manifolds are the central geometric objects in modern mathematics. An attempt to understand the nature of manifolds leads to many interesting questions. One of the most obvious questions is the following. Let M and N be manifolds: how can we decide whether M and N are ho topy equivalent or homeomorphic or di?eomorphic (if the manifolds are smooth)? The prototype of a beautiful answer is given by the Poincar´ e Conjecture. If n N is S ,the ndimensional sphere, and M is an arbitrary closed manifold, then n it is easy to decide whether M is homotopy equivalent to S . Thisisthecaseif and only if M is simply connected (assumingn> 1, the case n = 1 is trivial since 1 every closed connected 1dimensional manifold is di?eomorphic toS ) and has the n homology of S . The Poincar´eConjecture states that this is also su?cient for the n existenceof ahomeomorphism fromM toS . For n = 2this followsfromthewe known classi?cation of surfaces. Forn> 4 this was proved by Smale and Newman in the 1960s, Freedman solved the case in n = 4 in 1982 and recently Perelman announced a proof for n = 3, but this proof has still to be checked thoroughly by the experts. In the smooth category it is not true that manifolds homotopy n equivalent to S are di?eomorphic. The ?rst examples were published by Milnor in 1956 and together with Kervaire he analyzed the situation systematically in the 1960s
Differential algebraic topology : from stratifolds to exotic spheres by
Matthias Kreck(
Book
)
9 editions published in 2010 in English and held by 173 WorldCat member libraries worldwide
"This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, socalled stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincaré duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7spheres."Publisher's description
9 editions published in 2010 in English and held by 173 WorldCat member libraries worldwide
"This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, socalled stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincaré duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7spheres."Publisher's description
Eine Invariante für stabil parallelisierte Mannigfaltigkeiten by
Matthias Kreck(
Book
)
13 editions published between 1972 and 1973 in German and Undetermined and held by 56 WorldCat member libraries worldwide
13 editions published between 1972 and 1973 in German and Undetermined and held by 56 WorldCat member libraries worldwide
Positive Krümmung und Topologie by
Matthias Kreck(
Book
)
4 editions published in 1994 in German and held by 50 WorldCat member libraries worldwide
4 editions published in 1994 in German and held by 50 WorldCat member libraries worldwide
Cutting and pasting of manifolds; SKgroups by
U Karras(
Book
)
4 editions published in 1973 in English and held by 20 WorldCat member libraries worldwide
4 editions published in 1973 in English and held by 20 WorldCat member libraries worldwide
Eine Invariante für stabil parallelistierte Mannigfaltigkeiten : Matthias Kreck. by
Matthias Kreck(
Book
)
1 edition published in 1973 in German and held by 6 WorldCat member libraries worldwide
1 edition published in 1973 in German and held by 6 WorldCat member libraries worldwide
Topology : 31.8. bis 5.9. 1987(
Book
)
2 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
A guide to the classification of manifolds by
Matthias Kreck(
Book
)
1 edition published in 1997 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 3 WorldCat member libraries worldwide
Stable prime decompositions of fourmanifolds by
Matthias Kreck(
Book
)
1 edition published in 1994 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 1994 in German and held by 3 WorldCat member libraries worldwide
Classification and unstable classification of manifolds: some examples by
Matthias Kreck(
Book
)
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
Counterexamples to the Kneser conjecture in dimension four by
Matthias Kreck(
Book
)
1 edition published in 1994 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 1994 in German and held by 3 WorldCat member libraries worldwide
Mein Mietnomade und ich by
Matthias Kreck(
Book
)
2 editions published in 2012 in German and held by 3 WorldCat member libraries worldwide
Seine Welt ist die Logik  Martin Beck ist Professor für Mathematik. Dann aber vermietet er seine Mainzer Wohnung an Jörg Kaiser und nichts ist mehr logisch. Dabei war ihm Kaiser zunächst sehr sympathisch: weil er intelligent ist und so schöne altmodische Redewendungen gebraucht. Dann aber zahlt Kaiser monatelang keine Miete. Und auch keinen Strom  er zahlt überhaupt nichts. Die rechtlichen Mittel sind schnell ausgeschöpft und der Mieter ist immer noch in der Beckschen Wohnung. Wie Professor Dr. Martin Beck (d.i. der Autor, Professor Dr. Matthias Kreck) es schafft, seinen Mietnomaden mit Beharrlichkeit, Witz und  jawoll!  Logik aus seiner Wohnung zu bekommen. Wobei er auch vor unkonventionellen Methoden nicht zurückschreckt ... Matthias Kreck, geb. 1947, ist Mathematiker. Nach der Promotion studierte er evangelische Theologie, kehrte aber danach wieder in die Mathematik zurück. Er hat eine Professur an der Universität Bonn und lebt in Mainz und Bonn. In seiner Freizeit spielt er Cello
2 editions published in 2012 in German and held by 3 WorldCat member libraries worldwide
Seine Welt ist die Logik  Martin Beck ist Professor für Mathematik. Dann aber vermietet er seine Mainzer Wohnung an Jörg Kaiser und nichts ist mehr logisch. Dabei war ihm Kaiser zunächst sehr sympathisch: weil er intelligent ist und so schöne altmodische Redewendungen gebraucht. Dann aber zahlt Kaiser monatelang keine Miete. Und auch keinen Strom  er zahlt überhaupt nichts. Die rechtlichen Mittel sind schnell ausgeschöpft und der Mieter ist immer noch in der Beckschen Wohnung. Wie Professor Dr. Martin Beck (d.i. der Autor, Professor Dr. Matthias Kreck) es schafft, seinen Mietnomaden mit Beharrlichkeit, Witz und  jawoll!  Logik aus seiner Wohnung zu bekommen. Wobei er auch vor unkonventionellen Methoden nicht zurückschreckt ... Matthias Kreck, geb. 1947, ist Mathematiker. Nach der Promotion studierte er evangelische Theologie, kehrte aber danach wieder in die Mathematik zurück. Er hat eine Professur an der Universität Bonn und lebt in Mainz und Bonn. In seiner Freizeit spielt er Cello
Positive Krümmung und Topologie differenzierbarer Mannigfaltigkeiten by
Matthias Kreck(
Book
)
2 editions published in 1991 in German and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in German and held by 2 WorldCat member libraries worldwide
Nonconnected moduli spaces of positive sectional curvature metrics by
Matthias Kreck(
Book
)
3 editions published in 1992 in English and German and held by 2 WorldCat member libraries worldwide
3 editions published in 1992 in English and German and held by 2 WorldCat member libraries worldwide
Cancellation of lattices and finite twocomplexes by I Hambleton(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Differenzierbare Strukturen und die KervaireInvariante by
Matthias Kreck(
)
1 edition published in 2010 in German and held by 1 WorldCat member library worldwide
1 edition published in 2010 in German and held by 1 WorldCat member library worldwide
On the homeomorphism classification of smooth knotted surfaces in the 4sphere by
Matthias Kreck(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Arbeitsgemeinschaft GeyerHarder über 4Mannigfaltigkeiten 7.10. bis 13.10.1984(
Book
)
1 edition published in 1984 in German and held by 1 WorldCat member library worldwide
1 edition published in 1984 in German and held by 1 WorldCat member library worldwide
Eine Invariante fur stabil parallelisierte Mannigfaltigkeiten. Uberarbeitete Fassung 1973 by
Matthias Kreck(
Book
)
1 edition published in 1972 in German and held by 1 WorldCat member library worldwide
1 edition published in 1972 in German and held by 1 WorldCat member library worldwide
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Associated Subjects
Algebraic topology Cell aggregationMathematics Cobordism theory Curvature Diffeomorphisms Differential invariants Differential topology Fiber bundles (Mathematics) Global differential geometry Invariants Ktheory Lie groups Manifolds (Mathematics) Mathematics Noncommutative differential geometry Novikov conjecture Tangent bundles