Let C be a chain complex over a commutative ring R. Let M be a subchain of C such that M is chain equivalent to the zero chain complex. Must C/M and C be chain equivalent ?

Kolby Castillo 2022-09-26 Answered
Let C be a chain complex over a commutative ring R. Let M be a subchain of C such that M is chain equivalent to the zero chain complex. Must C/M and C be chain equivalent ?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Willie Sharp
Answered 2022-09-27 Author has 8 answers
Step 1
Take complexes of abelian groups:
C := 0 Z × 2 Z 0 ,
M := 0 Z × 2 2 Z 0 ,
C / M := 0 0 Z / 2 Z 0 .
Step 2
Then M is isomorphic to the complex
0 Z id Z 0 ,
which is contractible (homotopy equivalent to the zero complex), but there are no nonzero maps C / M C, so C and C/M are not homotopy equivalent.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-11-01
Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
asked 2021-03-02
In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference
asked 2021-10-27
Suppose you took random samples from three distinct age groups. Through a survey, you determined how many respondents from each age group preferred to get news from T.V., newspapers, the Internet, or another source (respondents could select only one mode). What type of test would be appropriate to determine if there is sufficient statistical evidence to claim that the proportions of each age group preferring the different modes of obtaining news are not the same? Select from tests of independence, homogeneity, and goodness-of-fit.
Since we are interested in proportions, the test for homogeneity is appropriate. Since we are determining if the current distribution fits the previous distribution of responses, the goodness-of-fit test is appropriate.
Since we can claim all the variables are independent, the test of independence is appropriate.
asked 2021-10-08
please explain this two situation without making any calculations.
c. 200 autistic children were given an IQ test. The researcher wants to compare their average IQ to IQ of the general public. Which hypothesis test should they use and why? d. Do you prefer to have high Type I error or high Type II error in your hypothesis test? Why?
asked 2021-01-27
Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group (1 point each) a. Compare the proportion of U.S. adults who have a positive opinion about the media versus those who have a negative opinion about the media. A) Comparing proportions for two groups B) Comparing two proportions from the same group b. Compare the proportion of female students at a university who live in a dorm to the proportion of male students at a university who live in a dorm A) Comparing proportions for two groups B) Comparing two proportions from the same group
asked 2020-12-12
Ozone The Environmental Protection Agency is examin- ing the relationship between the ozone level (in parts per million) and the population (in millions) of U.S. cities.
Part of the regression analysis is shown.
Dependent variable is: Ozone
R-squared =84.4%
s=5.454 with 162=14 df
Variable Coefficient SE(Coeff)
Intercept 18.892 2.395
Pop 6.650 1.910
a) We suspect that the greater the population of a city, the higher its ozone level. Is the relationship significant? Assuming the conditions for inference are satisfied, test an appropriate hypothesis and state your conclu- sion in context.
b) Do you think that the population of a city is a useful predictor of ozone level? Use the values of both R2 and s in your explanation.
asked 2021-01-06

Give the correct answer and solve given
a. Test for a difference in the means in the two populations using an [α=.05ttest.]
b. Place a 95% confidence interval on the difference in the means of the two populations.
c. Compare the inferences obtained from the results from the Wilcoxon rank sum test and the -test.
d. Which inferences appear to be more valid, inferences on the means or the medians?

New questions