The homology of manifolds enjoys a remarkable symmetry: Poincar??? duality. If the manifold is triangulated, then this duality can be established by associating to a s- plex its dual block in the barycentric subdivision. In a manifold, the dual block is a cell, so the chain complex based on the dual blocks computes the homology of the manifold. Poincar??? duality then serves as a cornerstone of manifold classi cation theory. One reason is that it enables the de nition of a fundamental bordism inva- ant, the signature. ...
Read More
The homology of manifolds enjoys a remarkable symmetry: Poincar??? duality. If the manifold is triangulated, then this duality can be established by associating to a s- plex its dual block in the barycentric subdivision. In a manifold, the dual block is a cell, so the chain complex based on the dual blocks computes the homology of the manifold. Poincar??? duality then serves as a cornerstone of manifold classi cation theory. One reason is that it enables the de nition of a fundamental bordism inva- ant, the signature. Classifying manifolds via the surgery program relies on modifying a manifold by executing geometric surgeries. The trace of the surgery is a bordism between the original manifold and the result of surgery. Since the signature is a b- dism invariant, it does not change under surgery and is thus a basic obstruction to performing surgery. Inspired by Hirzebruch's signature theorem, a method of Thom constructs characteristic homology classes using the bordism invariance of the s- nature. These classes are not in general homotopy invariants and consequently are ne enough to distinguish manifolds within the same homotopy type. Singular spaces do not enjoy Poincar??? duality in ordinary homology. After all, the dual blocks are not cells anymore, but cones on spaces that may not be spheres. This book discusses when, and how, the invariants for manifolds described above can be established for singular spaces.
Read Less
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
17987109900
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Contains: Illustrations, black & white. Springer Monographs in Mathematics . XII, 264 p. 14 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
17987532238
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . XII, 264 p. 14 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
17986272690
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Contains: Illustrations, black & white. Springer Monographs in Mathematics . XII, 264 p. 14 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
10830378561
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Print on demand Contains: Illustrations, black & white. Springer Monographs in Mathematics . XII, 264 p. 14 illus. Intended for professional and scholarly audience.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Print on demand Sewn binding. Cloth over boards. 264 p. Contains: Unspecified, Illustrations, black & white, Tables, black & white. Springer Monographs in Mathematics.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
17988165689
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . XII, 264 p. 14 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
17383449435
Shipping Options:
Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. 264 p. Springer Monographs in Mathematics . 7 Tables, black and white; 14 Illustrations, black and white; XII, 264 p. 14 illus. Intended for professional and scholarly audience.
