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Jun
10 |
awarded | Nice Question |
Feb
20 |
awarded | Popular Question |
Feb
9 |
awarded | Good Answer |
Nov
21 |
awarded | Yearling |
Oct
30 |
awarded | Pundit |
Jul
2 |
awarded | Curious |
Nov
22 |
answered | Is there a good way to understand the free loop space of a sphere? |
Nov
21 |
awarded | Yearling |
Oct
10 |
revised |
Are Sasakian metrics (associated to bumpy metrics) bumpy?
added 1 characters in body |
Oct
10 |
asked | Are Sasakian metrics (associated to bumpy metrics) bumpy? |
Sep
6 |
revised |
Cobordism and finite sheeted covers of manifolds
question made more specific |
Sep
5 |
comment |
Cobordism and finite sheeted covers of manifolds
The fact that characteristic numbers (Pontrjagin and Stiefel-Whitney numbers) determine cobordism classes completely is true for compact, oriented manifolds. What is a reference for this being true for manifolds which are not necessarily compact? |
Sep
5 |
comment |
Cobordism and finite sheeted covers of manifolds
@ Sam - Thanks! I made the necessary changes. |
Sep
5 |
revised |
Cobordism and finite sheeted covers of manifolds
added 21 characters in body |
Sep
5 |
asked | Cobordism and finite sheeted covers of manifolds |
Aug
30 |
comment |
loop space homology and lens spaces
Do you mean for each component of the free loop space? The free loop space $LM$ has $p$ components for the lens space $M=L(p,q)$. |
Jun
25 |
awarded | Promoter |
May
13 |
awarded | Good Question |
Feb
19 |
comment |
Homology of classifying space of spin group BSpin(n)
@Xiao-Gang : Write the spectral sequence (in homology) for the fibration $G\to EG\to BG$. It will follow from the $E^5$ and $E^6$ page that $H_5(BSpin(n);\mathbb{Z})=H_4(Spin(n);\mathbb{Z})$ and $H_6(BSpin(n);\mathbb{Z})=H_5(Spin(n);\mathbb{Z})$. It follows from Milnor-Moore (with your input on the homotopy groups of $Spin(n)$) that these are torsion groups. Now you just have to compute these! |
Feb
19 |
comment |
Homology of classifying space of spin group BSpin(n)
@Xiao-Gang : Write the spectral sequence (in homology) for the fibration $G\to EG\to BG$. It will follow from the $E^5$ and $E^$ page that $H_5(BSpin(n);\mathbb{Z})=H_4(Spin(n);\Z)$ and $H_6(BSpin(n);\mathbb{Z})=H_5(Spin(n);\Z)$. It follows from Milnor-Moore (with your input on the homotopy groups of $Spin(n)$) that these are torsion groups. Now you just have to compute these! |