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For Questions 1-5, for each space X, a) Describe a A-compex structure for the space X and b) Compute its homology groups H₂(X) for i = 0, 1, 2, 3. c) Compute the Betti numbers 3; (X) for i = 0, 1, 2, 3. 1) X = S² V S¹ where S" is n-sphere. 2) X = T² V D² where T² is 2-torus and D² is closed 2-disk. 3) X = ₂ closed, orientable genus-2 surface. 4) X = K² Klein bottle. 5) X = S³

For Questions 1-5, for each space X, a) Describe a A-compex structure for the space X and b) Compute its homology groups H₂(X) for i = 0, 1, 2, 3. c) Compute the Betti numbers 3; (X) for i = 0, 1, 2, 3. 1) X = S² V S¹ where S" is n-sphere. 2) X = T² V D² where T² is 2-torus and D² is closed 2-disk. 3) X = ₂ closed, orientable genus-2 surface. 4) X = K² Klein bottle. 5) X = S³

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For Questions 1-5, for each space X, a) Describe a A-compex structure for the space X and b) Compute its homology groups H;(X) for i = 0, 1, 2, 3. c) Compute the Betti numbers B:(X) for i = 0,1,2, 3. 1) X = S? v S' where S" is n-sphere. 2) X = T² V D² where T2 is 2-torus and D² is closed 2-disk. 3) X = E2 closed, orientable genus-2 surface. 4) X = K? Klein bottle. 5) X = S3
Transcribed Image Text:For Questions 1-5, for each space X, a) Describe a A-compex structure for the space X and b) Compute its homology groups H;(X) for i = 0, 1, 2, 3. c) Compute the Betti numbers B:(X) for i = 0,1,2, 3. 1) X = S? v S' where S" is n-sphere. 2) X = T² V D² where T2 is 2-torus and D² is closed 2-disk. 3) X = E2 closed, orientable genus-2 surface. 4) X = K? Klein bottle. 5) X = S3
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