26

votes

answer

1k

views

$V$, $W$ are varieties. Does $V\times \mathbf{P}^1=W\times \mathbf{P}^1$ imply $V=W$?

ag.algebraic-geometry

oct 15 11 at 23:30 Francesco Polizzi 19.2k●2●36●56

7

votes

4

answers

540

views

How does all of the bundles over a certain manifold characterize the homotopy class of the base manifold?

differential-topology at.algebraic-topology

apr 21 11 at 7:36 Oscar Randal-Williams 5,409●1●14●28

6

votes

2

answers

361

views

Can a smooth, immersed loop in R^2 become not nullhomotopic by removing a point?

dg.differential-geometry homotopy-theory differential-topology

mar 12 11 at 10:33 Bruno Martelli 5,026●1●14●34

2

votes

2

answers

554

views

Can we deduce that two rings R1 and R2 are isomorphic if their polynomial ring is iso.?

ra.rings-and-algebras

dec 8 10 at 14:11 Steven Landsburg 9,551●1●29●52

1

vote

2

answers

217

views

Contractible noncompact 3-manifold without boundary not homeomorphic to $\Bbb R^3$

differential-topology reference-request

nov 25 11 at 1:18 lethe 448●3●8

Questions

$V$, $W$ are varieties. Does $V\times \mathbf{P}^1=W\times \mathbf{P}^1$ imply $V=W$?

How does all of the bundles over a certain manifold characterize the homotopy class of the base manifold?

Can a smooth, immersed loop in R^2 become not nullhomotopic by removing a point?

Can we deduce that two rings R1 and R2 are isomorphic if their polynomial ring is iso.?

Contractible noncompact 3-manifold without boundary not homeomorphic to $\Bbb R^3$