Problem 1. For each of the following abstract simplicial complexes, sketch the geometric realization (up to homoeomorphism) and compute the Euler charac- teristic: a. {[a], [b], [c], [a, b]}, b. {[a], [b], [a, b]}, c. {[a], [b], [c], [d], [a, b], [c, d]}, d. {[a], [b], [c], [d], [a, b], [b, c], [a, c], [c, d]}, e. {[a], [b], [c], [a, b], [b, c], [a, c], [a, b, c]}. Which pairs of these simplicial complexes have homotopy equivalent geometric realizations? Which pairs have equal Euler characteristics?
Problem 1. For each of the following abstract simplicial complexes, sketch the geometric realization (up to homoeomorphism) and compute the Euler charac- teristic: a. {[a], [b], [c], [a, b]}, b. {[a], [b], [a, b]}, c. {[a], [b], [c], [d], [a, b], [c, d]}, d. {[a], [b], [c], [d], [a, b], [b, c], [a, c], [c, d]}, e. {[a], [b], [c], [a, b], [b, c], [a, c], [a, b, c]}. Which pairs of these simplicial complexes have homotopy equivalent geometric realizations? Which pairs have equal Euler characteristics?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Problem 1. For each of the following abstract simplicial complexes, sketch the
geometric realization (up to homoeomorphism) and compute the Euler charac-
teristic:
a. {[a], [b], [c], [a, b]},
b. {[a], [b], [a, b]},
c. {[a], [b], [c], [d], [a, b], [c, d]},
d. {[a], [b], [c], [d], [a, b], [b, c], [a, c], [c, d]},
e. {[a], [b], [c], [a, b], [b, c], [a, c], [a, b, c]}.
Which pairs of these simplicial complexes have homotopy equivalent geometric
realizations? Which pairs have equal Euler characteristics?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e25041d-7573-46df-b9d3-ec2dd7694c16%2F5beecdc7-7fa9-4e56-bbe3-667bfdb590e4%2Faxt91ph_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. For each of the following abstract simplicial complexes, sketch the
geometric realization (up to homoeomorphism) and compute the Euler charac-
teristic:
a. {[a], [b], [c], [a, b]},
b. {[a], [b], [a, b]},
c. {[a], [b], [c], [d], [a, b], [c, d]},
d. {[a], [b], [c], [d], [a, b], [b, c], [a, c], [c, d]},
e. {[a], [b], [c], [a, b], [b, c], [a, c], [a, b, c]}.
Which pairs of these simplicial complexes have homotopy equivalent geometric
realizations? Which pairs have equal Euler characteristics?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 8 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
